(Reuters) - America's government-controlled mortgage financegiants, Fannie Mae and Freddie Mac, will likely guarantee a shrinking share of new loans over the next decade, congressional analysts said on Tuesday.

During the 2007-09 financial crisis, it was almost impossible for home buyers to get a loan without a government guarantee, andFannie Mae and Freddie Mac stepped into the breach, backing roughly 60 percent of new mortgages between 2008 and 2013.

But a mix of recent increases in fees charged by the two firms and a renewed willingness to lend by private sources of capital will help shrink Fannie Mae and Freddie Mac's share to about 40 percent by 2024, the Congressional Budget Office said in a report.

The two firms do not loan directly but rather buy loans which they then resell in bundles. They substantially hiked the fees they charge to guarantee mortgages in 2011 and 2012, reducing their advantage over private-sector firms.

Their market share is already shrinking, falling to about 50 percent of new mortgages in the first half of 2014, the CBO said, citing data from Inside Mortgage Finance.

The CBO also examined several scenarios for reforming the U.S. mortgage financelandscape, including replacing Fannie Mae and Freddie Mac with a government entity or eliminating them entirely.

But because the CBO thinks the private market would likely price fees similarly to Fannie Mae and Freddie Mac, the congressional analysts thought none of the scenarios would have a big impact on the federal budget.