by Jonathan Weisman

WASHINGTON — The Senate, with broad bipartisan support, voted overwhelmingly Tuesday to expand the reach of the landmark Violence Against Women Act of 1994 by fortifying the power of American Indian tribal courts and explicitly protecting gay victims of domestic abuse.

The 78-to-22 vote raised the pressure on the House to act and expanded by 10 votes the margin of approval that a nearly identical bill garnered in the Senate last April. Twenty-three Republicans backed the measure on Tuesday, up from 15 last year. The vote came after 17 House Republicans on Monday wrote Speaker John A. Boehner of Ohio and Representative Eric Cantor of Virginia, the House majority leader, demanding immediate action on a domestic violence bill that could get bipartisan support, unlike the House bill that passed largely on party lines last year.

The new version “must reach all victims and perpetrators of domestic violence, dating violence, sexual assault and stalking in every community in the country,” the letter stated, echoing the language used by supporters of the Senate bill, which expands the law’s focus to include homosexual and American Indian victims and assailants.

The law, reauthorized twice before with almost no controversy, has been stuck this time in the broader fight over the size and scope of government, and a more specific battle over the powers Congress should afford tribal courts, which now cannot pursue non-Indians who attack Indian women on tribal land. Conservative groups like the Heritage Foundation and the Independent Women’s Forum have blasted the law as an ineffective waste of money and the new version as a dangerous expansion of governmental powers.

“I never thought the day would come when this issue would become politicized, but I’m afraid it has,” said Senator John Cornyn, Republican of Texas, as he led conservative opposition to the bill.

But the 2012 election results — and the yawning gender gap that kept the White House in President Obama’s hands, expanded Democratic control of the Senate and chipped away at the Republicans’ House majority — may have changed the political dynamics on the antiviolence bill.

“Quite honestly, we can’t afford to be sitting on this for months or another year,” said Senator Lisa Murkowski, Republican of Alaska and a supporter of the Senate bill.

After the vote, President Obama called on the House to act.

“Delay isn’t an option when three women are still killed by their husbands or boyfriends every day,” the president said in a statement. “Delay isn’t an option when countless women still live in fear of abuse, and when one in five have been victims of rape. This issue should be beyond debate — the House should follow the Senate’s lead and pass the Violence Against Women Act right away. This is not a Democratic or Republican issue — it’s an issue of justice and compassion.”

House Republican leaders find themselves squeezed between moderate — and many conservative — Republicans who want to put the issue behind them and some senior Republicans who remain adamantly opposed to reauthorizing the act. Aides to Mr. Cantor have been meeting with both sides for weeks, and say they will not move legislation to the House floor until both sides sign off on a bill that will have broad support.

The biggest sticking point is the expansion of tribal court authority, which many Republicans see as an unconstitutional power grab by the tribes that will deprive non-Indians of their fundamental constitutional rights. Social conservatives object to a provision in the Senate bill that clarifies that victims rights and prosecution programs created by the law can be used in cases of domestic abuse involving same-sex couples.

But as senior Republican leaders like Mr. Cantor urge their party to project a more can-do image on issues beyond budget cuts and taxes, moderate Republicans say a bill like the Violence Against Women Act is a crucial test.

“At a time like this, we have to show we can get something done,” said Representative Charlie Dent of Pennsylvania, one of the signers of the House letter. And, he added, legislation like the Violence Against Women Act “should not be a heavy lift.”

This article has been revised to reflect the following correction:

Correction: February 12, 2013

An earlier version of this story included a statement from Vice President Joseph R. Biden Jr. that was attributed to the president. The current quotation is a statement from the president.