Florida Republican Sen. Marco Rubio reportedly will be the lead sponsor of a Senate bill to ban abortions after 20 weeks.

The decision follows Rubio’s efforts to lead the Senate in crafting, then passing immigration reform legislation last month and came at the urging of right-to-life groups, according to The Weekly Standard.

A staffer for the first-term senator and potential 2016 presidential candidate would neither confirm nor deny the story. However, the magazine said several sources confirmed that Rubio had agreed and that he would make an announcement when Congress returns from Fourth of July recess.

A late-term abortion measure passed the Republican-controlled House last month, and the Texas legislature is considering a similar measure.

Such a bill would face a tougher challenge in the Democrat-controlled Senate, but Rubio’s support would at least increase national attention on the issue.

Should Rubio run for president, such a sponsorship could help improve his standing among potential conservative voters who questioned his championing of the immigration bill.

Some recent poll numbers suggest support for a ban on late-term abortions.

A Gallup survey in January found that 64 percent of Americans thought an abortion in the second three months of pregnancy should be illegal. And 80 percent felt they should be banned in the last three months.

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