This was CNBC's live blog covering European markets.

European markets closed higher Tuesday, with the U.K.'s FTSE 100 hitting a fresh intraday record high as investors built on positive momentum in the previous session.

The pan-European benchmark Stoxx 600 index provisionally closed 1.1% higher, with all sectors bar mining trading in the green, as investors eyed strong euro zone business activity data and the potential for upcoming interest rate cuts.

The U.K.'s FTSE 100 marked an all-time intraday high of 8067.73 in early deals, before paring gains on hawkish comments made by the Bank of England's chief economist, Huw Pill. The index nonetheless extended the record close set on Monday, finishing at 8044.81 points.

Investors in the region are looking ahead to bank earnings this week, and will be keeping an eye on a range of tech earnings stateside, with Tesla reporting during U.S. trading hours Tuesday.

In Europe Tuesday, Renault, Kering, OVH, Novartis and Associated British Foods all reported earnings.

Overnight, Asia-Pacific markets extended gains from Monday as investors look toward flash business activity figures from Australia, Japan and India. U.S. stocks rose at Tuesday's open.

Europe stocks close higher

European stocks closed higher on Tuesday, with the benchmark Stoxx 600 index ending the session up by 1.1%.

Germany's DAX index led major bourses with a 1.6% gain, while France's CAC 40 rose 0.8%. The U.K.'s FTSE 100 set a second straight record close after climbing 0.25%.

— Jenni Reid

UK stocks lag major bourses, sterling climbs after BOE chief economist comments

U.K. stocks remained in positive territory on Tuesday afternoon, with the blue-chip FTSE 100 index 0.25% higher at 3:50 p.m. London time, after Bank of England Chief Economist Huw Pill delivered a speech that was perceived by many investors as hawkish.

Equity gains were lower than earlier in the session and lagged Germany's DAX index, which was up 1.35%, and France's CAC 40, up 0.7%.

U.K. stocks had powered ahead during Monday's session, taking the FTSE 100 to a record close on mounting expectations of a summer rate cut from the BOE.

Pill on Tuesday said that his baseline at the start of March was that "the time for cutting Bank Rate remained some way off."

"The combination of little news and the passage of time have brought a Bank Rate cut somewhat closer. But the same lack of news gives me no reason to depart from the baseline that I already established," he said.

The British pound, which fell 0.5% against the U.S. dollar on Monday, clawed back 0.7% on Tuesday.

— Jenni Reid

U.S. crude oil falls to lowest level since March, dips below 50-day moving average

U.S. crude oil hit a session low of $80.89 a barrel on Tuesday, the lowest level since late March.

The West Texas Intermediate futures contract for June also dipped below the 50-day moving average of $81.22 a barrel for the first time since early February.

WTI was last trading at $81.51 a barrel, down 39 cents, while the June Brent futures contract was last down 36 cents at $86.64 a barrel.

Traders have bid down prices after a runup early this month on fears that Iran and Israel were on the brink of war. Those fears have largely dissipated as the bitter enemies have signaled they are not interested in a wider war after trading tit-for-tat strikes this month.

The market was also unconcerned about looming oil sanctions on Iran. The House of Representatives passed legislation over the weekend that would target ports, vessels and refineries that accept Iranian oil. The Senate could take up the legislation this week.

— Spencer Kimball

U.S. stocks open higher

U.S. stocks opened higher on Tuesday, with Wall Street focused on a fresh slate of forthcoming tech earnings.

The S&P 500 added 0.4% shortly after the opening bell, while the Nasdaq Composite gained 0.4%. The Dow Jones Industrial Average climbed 124 points, or 0.3%.

— Brian Evans

Bank of England's chief economist says rate cut may be some way off

The Bank of England's chief economist Huw Pill struck a hawkish note Tuesday, indicating that a forthcoming interest rate cut might not come as soon as expected.

While falling inflation has brought a prospective cut "somewhat closer," Pill said there was more risk in cutting rates too quickly than too late.

"The combination of little news and the passage of time have brought a Bank Rate cut somewhat closer," Pill said in a speech to the University's of Chicago Booth School of Business, according to Reuters.

"But the same lack of news gives me no reason to depart from the baseline," he said, in reference to a previously stated more restrictive stance.

As recently as Monday, markets had been expecting an initial quarter-point cut from the Bank of England in August.

— Karen Gilchrist

Europe business activity improves

Euro zone business activity expanded in April as growth in the bloc's services sector offset weakness in manufacturing, new data showed Tuesday.

HCOB's preliminary composite euro zone purchasing managers' index, compiled by S&P Global, rose to 51.4 this month, up from 50.3 in March and ahead of the 50.7 anticipated.

Meantime, the U.K. business sector also showed signs of strength, with S&P Global's purchasing managers' index rising to a stronger-than-expected 54 in April, up from 52.8 the previous month.

— Karen Gilchrist

Stocks on the move: AB Foods up 9.5%, Randstad down 6%

Shares of Associated British Foods rose 9.5% after it raised its outlook and interim dividend amid easing inflationary pressures on its food brands and improved sales at high street retailer Primark.

Meantime, Dutch recruiter Randstad fell 6% following a bigger-than-expected fall in first-quarter earnings as hiring conditions weaken.

— Karen Gilchrist

Europe stocks open higher as FTSE hits record high

European stocks opened higher Tuesday, with the benchmark Stoxx 600 index up 0.6% by 8:05 a.m. London time.

The U.K.'s FTSE 100 climbed 0.5% to hit an all-time intraday high, while France's CAC 40 was 0.3% higher, and Germany's DAX up 0.8%.

— Karen Gilchrist

Novartis raises guidance after first-quarter results beat expectations

Swiss drugmaker Novartis raised its full-year guidance after reporting better-than-expected first-quarter results led by the success of products including heart failure drug Entresto and psoriasis drug Cosentyx.

The company said 2024 net sales were set to grow by a high-single to low double-digit percentage, while adjusted operating income was expected to grow by a low double-digit to mid-teens percentage.

It previously forecast adjusted operating income to increase by a "high single-digit" percentage and sales growth to rise by a "mid single-digit."

— Karen Gilchrist

Renault first-quarter sales rise 1.8%

French automaker Renault on Tuesday reported a 1.8% uptick in its first-quarter revenue, led by strong performance in its financing business.

The company sold 549,099 units in the three-month period, with revenue totaling 11.7 billion euros ($12.47 billion). That's slightly above a company-provided consensus of a slight annual drop to 11.49 billion euros.

— Karen Gilchrist

CNBC Pro: When Tesla shares fall — these 6 stocks tend to rise, according to recent history

Six stocks in the S&P 500 tend to rise when Tesla shares fall, according to an analysis of recent data by CNBC Pro.

The share price performance of these six stocks was inversely correlated to Tesla's last month. They have typically shot up this year, in contrast to a 40% plunge for Tesla.

CNBC Pro subscribers can read more about the six stocks here.

— Ganesh Rao

CNBC Pro: 'Bargain' energy stocks: Morningstar strategist picks 5 to buy as oil prices slide

Heightened geopolitical tensions have triggered volatility in crude oil prices, but one strategist is looking keenly for opportunities in the energy sector.

It was among the laggards last year, but things have turned around with many stocks now trading near all-time highs.

Stephen Ellis, energy and utilities strategist at Morningstar, said oil market volatility does present challenges and urged investors to be patient, which "regularly pays off within energy."

However, he did say there were "selective bargains" in the market currently and revealed five stocks in the energy space he likes right now.

CNBC Pro subscribers can read more here.

— Amala Balakrishner

European markets: Here are the opening calls

European markets are set to open in positive territory Tuesday, building on gains seen at the start of the new trading week.

The U.K.'s FTSE 100 index is expected to open 39 points higher at 8,070, Germany's DAX up 117 points at 17,969, France's CAC 36 points higher at 8,057 and Italy's FTSE MIB up 98 points at 33,628, according to data from IG.

Earnings are set to come from Renault, Kering, OVH and Novartis, and Associated British Foods releases interim results. On the data front, preliminary manufacturing and services purchasing managers' index data for the euro zone in April will be released.

— Holly Ellyatt