The Democratic House previously approved a measure to block the policy, also known by critics as the global gag rule, but it was stalled under Republicans in the Senate.
This month, Democrats reclaimed control of the Senate for the first time since 2015 by the slimmest of margins, with a 50-to-50 split and Vice President Kamala Harris able to break tie votes.
However, at least two Republicans, Senators Susan Collins of Maine and Lisa Murkowski of Alaska, also support legislation to permanently end the Mexico City policy, meaning “there might be a newer window to make something happen,” said Jen Kates, the director of global health and H.I.V. policy at the Kaiser Family Foundation.
“I think everyone will agree, whatever side they’re on, on the issue, is that the Ping-Ponging is a very challenging way to have this policy operate,” Ms. Kates said, discussing the work of nongovernmental organizations. “It provides no stability or predictability for N.G.O.s, and it’s disruptive.”
Opponents of abortion rights also want to see the matter become settled law, but in a way that enshrines the Mexico City policy to immediately prevent Mr. Biden and future presidents from supporting abortion providers abroad.
Last month, Senator Mike Lee, Republican of Utah, revived a plan he had introduced in previous congressional terms to make the funding ban permanent. In a Feb. 3 speech on the Senate floor, he said it was necessary to prevent the policy from being “rescinded and reinstated again and again between changing administrations.”
“The lives of babies and the dignity of women are not political footballs,” Mr. Lee said. “Women and unborn children everywhere have immeasurable dignity and worth, regardless of where they are from. And they ought to be entitled to the right to life and protection from harm — regardless of who is in office.”