A final, formal vote is scheduled for Wednesday. The bill will then move on to the Senate, where the Republican majority is also expected to approve the measure.
Democrats and women's rights activists have been protesting the bill for weeks. On June 25, Democratic Sen. Wendy Davis failed to win enough support in an effort to kill the anti-abortion bill with a filibuster.
"Over the past few years, we've seen relentless attacks on women's health and rights in the state of Texas," said Cecile Richards, President of Planned Parenthood Action Fund, in a statement. "Already, these attacks have hurt hundreds of thousands of women, and will hurt many more if the legislation the House approved tonight becomes law."
Richards continued, "With this vote, the Texas House of Representatives ignored not just the thousands of Texans who have spoken out against these attacks on women's health, but the vast majority of Texans."
The bill, which was outlined by Republican Rep. Jody Laubenberg, would require doctors to have admitting privileges at nearby hospitals, only allow abortions in surgical centers, dictate when abortion pills are taken and ban abortions after 20 weeks. Exceptions to the ban would only be allowed when the women's life was in imminent danger.