(Adds changes in proposal, Pelosi quote)

WASHINGTON, March 3 (Reuters) - Key U.S. House Democrats have agreed to changes in legislation letting bankruptcy judges reduce mortgage debt and hope to have a vote on the legislation on Thursday, House Financial Services Committee Chairman Barney Frank said on Tuesday.

“Changes were agreed to that I think made it better,” Frank, a Massachusetts Democrat, told Reuters after emerging from negotiations on the controversial bill with other lawmakers.

The bill, which had originally been expected to pass the House last week but was delayed while debate over it continued, was now “on track” to pass on Thursday, Frank said.

The bill represents one of many efforts under way in Congress and the Obama administration to tackle a stubborn housing market crisis that has dragged the U.S. economy into recession.

At present, the terms of mortgages on primary residences may not be altered in bankruptcy proceedings. Some lawmakers want to change this to help distressed mortgage borrowers stay in their homes.

The latest changes to the House bill would ensure that bankruptcy judges weigh whether banks had offered home loan modifications before the judges get involved in changing the terms of loans -- such as by setting longer payback terms or lower interest rates.

The changes were described in a letter by three other lawmakers who were involved in the negotiations and wrote to House lawmakers urging them to pass the amended bill.

“We have worked together to make improvements to the bill that will ensure we avoid bankruptcy whenever possible by first and foremost giving homeowners access to a systematic loan modification process,” wrote the three Democratic lawmakers, Rep. Zoe Lofgren, Rep. Ellen Tauscher and Rep. Dennis Cardoza.

“For those who cannot be helped in this process, they will be able to seek recourse in Chapter 13 (bankruptcy) through a uniform process.”

The legislation, often referred to as the “cramdown” bill, was supposed to be voted on last week but was pulled at the last minute after a faction of fiscal conservatives expressed misgivings about the plan. They said it could distort the price of mortgage investments on Wall Street.

Officials at the Federal Reserve and Federal Housing Finance Agency fret that giving bankruptcy judges sweeping power to modify home loans could discourage fresh investment in the sector, and many lawmakers share that view.

House Speaker Nancy Pelosi, trying to assuage lawmakers’ concerns, scheduled a briefing for them on Tuesday evening by Shaun Donovan, the secretary of Housing and Urban Development.

After the briefing, Pelosi told reporters the session had been “helpful ... for members to see how it (the legislation) fit in with the full picture of how we go forward and stabilize home ownership in America.”

President Obama has endorsed the cramdown idea as a useful tool to prod mortgage service companies to ease the terms of troubled loans but officials agree that it must be carefully calibrated.

Last week the President outlined a housing rescue plan that aims to lower monthly mortgage payments for 9 million borrowers and restore a housing market battered by record foreclosures.