Weatherford Republican Rep. Phil King says a process allowing pregnant teenagers to seek a court's permission -- instead of their parents' -- to have an abortion is "far from a best practice."
He urged a House panel Tuesday to tighten the law.
Others praise Texas' 1999 law, which enables hundreds of girls under 18 to get an abortion without telling their parents.
The committee heard King's bill making the law more-strict, but didn't immediately approve it to the full House.
Abortion rights groups say the cases are rare but the process is necessary for girls who are abandoned or abused.
King asked lawmakers how they'd feel if their child got an abortion without telling them.
Houston Democratic Rep. Jessica Farrar said, "We're dealing with parents that have failed their children."