Sen. Majority Leader Harry M. Reid (D-Nev.) said Wednesday that the Senate will consider a bill to add $6 billion to the Federal Emergency Management Administration’s Disaster Relief Fund, a move that could result in a fast action to replenish the fund but is also designed to put pressure on Republicans who have argued additional FEMA funding should be paid by offsetting spending cuts.

His comments came as House Majority Leader Eric Cantor (R-Va.) pushed back against any perception that Republicans were opposed to additional FEMA funding.

Cantor insisted disaster victims, who include residents of his own Virginia district hit hard by Hurricane Irene, would get FEMA funds.

“I have never, never said that I’m holding anything hostage or would be for playing politics with this. It is inaccurate and I think it is irresponsible on part of those who have written that,” Cantor said.

He told reporters Wednesday that his goal has been to end what had become an annual exercise of underfunding FEMA at the beginning of each fiscal year and then returning with a request for emergency dollars at the end of the year when disasters had sapped the fund.

Reid’s and Cantor’s remarks taken together suggest Congress may find a rare area of bipartisan agreement in coming days to refill the stressed disaster relief fund.

The House had insisted that additional FEMA funding should be offset with spending cuts elsewhere. It approved an appropriations measure in June that included $3.65 billion to refresh the disaster fund, but cut FEMA grants to local first responders and a program to encourage energy efficient cars to pay for the infusion.

But Cantor said the Budget Control Act, the spending deal agreed to in early August by Congress as part of a compromise to allow debt ceiling to rise, specifically allows funding for disasters outside of discretionary spending capped under the agreement.

He said that when President Obama informs Congress how much more FEMA needs than the $1.8 billion he had requested in the spring, Congress now has “in place a mechanism” to approve it.

FEMA’s fund has dipped to $566 million, even as a string of destructive natural disasters has increased demand for federal dollars to help local governments and individuals.

The Senate had advanced its larger $6 billion proposal for the fund in a $41 billion measure to fund homeland security efforts. It was being considered at the committee level Wednesday.

Reid told reporters Wednesday that he will break the funding out and put forward a bill dealing with the disaster relief funding alone.

“We need to get this relief funding to the American people as quickly as we can,” Reid said. “And we’re going to do that. I’m going to bring a free-standing bill that we’re going to have a chance to vote on.”

Following Reid’s remarks, Cantor said in a statement that Reid should provide more information about his proposal for a standalone bill to the House.

“I would ask Leader Reid to provide members of the House with the details of his request and a breakdown of what immediate funding is needed for each of the specific disaster areas listed above, so that the House can appropriately act on any legislation passed by the Senate. I appreciate Leader Reid’s concern for the people of my district and those facing these terrible disasters across the country, and hope we can work quickly and responsibly to provide any funding needed immediately, as well as to navigate through the appropriations process for the coming year,” he said.

Cantor said the House “stands ready” to provide immediate funding needed by disaster victims.

This story has been updated.