By opening the doors to highly educated immigrants, the bill being debated in the Senate will disadvantage women without access to education according to Sen. Mazie Hirono (D-Hawaii). (The Fold/The Washington Post)

A group of female senators is planning to introduce a proposal Thursday that would ensure that more women would be admitted to the United States under a comprehensive immigration bill, representing an early attempt at leverage by the Senate’s emerging bloc of women.

The lawmakers say pending immigration legislation is unfairly weighted toward male workers because it rewards applicants who are better educated and have more technical skills.

Under their amendment, the female senators propose reserving 30,000 residency cards each year for fields in which women hold most of the jobs, such as nannies, home health-care workers and early childhood educators.

At least 12 women have signed on to co-sponsor the amendment, including Sen. Lisa Murkowski (R-Alaska), whom Democrats hope will play a key role in winning more GOP support, aides said. The Senate has a record contingent of 20 women this session, 16 of whom are Democrats.

“For this immigration bill to institutionalize and set in concrete the unequal opportunities women have in other countries is not the way to go,” Sen. Mazie Hirono (D-Hawaii), who developed the amendment with Sen. Patty Murray (D-Wash.), said in an interview.

The amendment is one of dozens the Senate will consider as the immigration bill progresses through a second week of debate on the chamber floor. Proponents are trying to keep intact a bipartisan coalition championing the most far-reaching overhaul of immigration law in nearly three decades.

On Wednesday, the Senate voted on 10 amendments, defeating a border security measure sponsored by Sen. Rand Paul (R-Ky.) that would have required Congress to assess progress on border security operations annually before a new group of illegal immigrants could earn work visas.

Chamber leaders also delayed a key vote on a strict border security proposal from Sen. John Cornyn (R-Tex.) that Democrats oppose. Other Republicans are working on several border control amendments that are expected to be controversial but could help win GOP support for the bill.

Comprising 20 percent of the chamber, female senators have made inroads into leadership ranks by chairing nine committees, including Sen. Barbara Mikulski (D-Md.) on the Appropriations Committee and Murray on the Budget Committee.

Murray said female senators have influenced other high-profile policy debates, including the Violence Against Women Act, in which the four female Republicans joined Democrats in voting to reauthorize the law.

“We’re finding that as more women come here and move into positions of leadership, we may see a problem that all-male panels don’t and we bring it to the forefront,” Murray said.

On immigration, Hirono and Murray said they are intent on fixing a problem that is being created by the shift, under the Senate legislation, away from extended family members of U.S. citizens in favor of immigrants with higher levels of education and more technical skills.

The Senate plan would eliminate three categories of residency, or green, cards for married adult children, siblings of U.S. citizens and a random “diversity lottery.” They would be replaced with a “merit-based” system that awards points to applicants based on work skills and family connections.

All told, up to 250,000 visas would be distributed on the points system based on the unemployment rate. Advocates have said women are at a disadvantage under this system because they face cultural discrimination in their home countries that makes it more difficult for them to gain access to higher education and high-tech training.

Karen Panetta, vice president of the Institute of Electrical and Electronics Engineers, argued during testimony to a Senate committee in March that men make up as much as 85 percent of the foreign workers awarded visas under the H-1B program for high-tech program. The U.S. government does not compile such statistics; the Senate bill would require the Department of Homeland Security to begin reporting the ratio annually.

Panetta said in an interview that she appreciates the proposal to create a new category of green cards reserved for fields where women outnumber men, but added that more must be done to even the playing field.

The Senate bill would increase the H-1B program from 65,000 visas to as many as 180,000 in coming years, and the Hirono-Murray amendment would do nothing to address potential gender imbalances in that category.

“I think that being a historic woman in the Senate, they would understand the challenges facing women trying to come into non-traditional fields for women,” said Panetta, who has been reaching out to the offices of the 20 women in the Senate.

The Hirono-Murray amendment faces a tough path in a Senate because the legislation would limit the number of visas, pitting the proposal against other categories.

Mee Moua, president of the Asian American Justice Center, said her organization has considered compiling all the immigration amendments that affect women and creating an “omnibus women’s proposal” that female lawmakers could champion.

Hirono is the Senate’s only first-generation immigrant, having been moved from Japan to Hawaii when she was 7 years old by her mother, who was fleeing an abusive husband. She said her experience has influenced her thinking, especially in trying to protect female heads of households who want to come to the United States.

Hirono said her mother, who was born in Hawaii, won a legal ruling that she was a U.S. citizen. Without that decision, the senator said, “she never would have been able to come here” under the current Senate proposal.

Ed O’Keefe and Brook Silva-Braga contributed to this report.