President Barack Obama on Tuesday called on Congress to overhaul the nation's decades-old mortgage finance system and wind down government-backed Fannie Mae and Freddie Mac.

Since the housing market has started to rebound, with far fewer foreclosures and rising home values, the White House wants to help spur the recovery. Obama unveiled a new strategy that ultimately places the mortgage finance system more in the hands of the private sector than backed by the government.

“Housing prices don’t keep going on up forever at the kind of pace it was going up. It was crazy,” Obama said. “One of the key things to make sure it doesn’t happen again is to wind down these companies. They’re not really government but not really private sector; they’re known as Freddie Mac and Fannie Mae. For too long, these companies were allowed to make huge profits buying mortgages knowing that if their bets went bad taxpayers would be left holding the bag.”

Obama lauded a “bipartisan group of senators working to end Fannie and Freddie as we know it.”

He said that he intends to build a “rock solid foundation to make sure the kind of crisis we went through never happens again.”

Below are highlights of the Obama administration's housing plans:

Expand refinancing programs

The administration is reinvigorating its effort to help borrowers who owe more on their homes than they are worth by pushing for an expansion of refinancing for those who purchased homes when rates were above the current historic lows. By refinancing, borrowers could save hundreds of dollars a month, adding to their disposable income and stimulating the economy, officials said.

So far, legislative efforts to expand refinancing programs have failed in Congress. The White House has said there is increasing pressure for Congress to act now that mortgage rates have started to increase, which would reduce the savings generated by refinancing.

If Obama's nominee to oversee Fannie Mae and Freddie Mac, veteran Democratic Representative Mel Watt, wins confirmation in the full Senate, he would be able to oversee some refinancing programs administratively without the help of Congress.

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Help qualified families get mortgages

Obama insists that any future U.S. housing system must ensure the popular 30-year fixed rate mortgage is widely available to borrowers. Without some government backstop, that mortgage term could become exceedingly rare.

Fannie Mae and Freddie Mac do not make loans, but provide financing to banks and other lenders by purchasing mortgages, which they either hold or repackage as securities that are sold to investors with a guarantee.

Obama wants to end Fannie Mae and Freddie Mac, yet still maintain government guarantees. The government guarantees offered by the two mortgage companies makes it hard for private financial firms to compete since banks don't want to lend for long durations without the federal backstop.

Reform immigration system

Not often discussed in connection with the housing market, Obama says there is a need to fix the immigration system. White House officials say immigration reform would enable currently undocumented immigrants to purchase properties, leading to rising home values and spurring the broader housing recovery.

The Senate has passed a bipartisan immigration bill that's supported by many business leaders, labor, and law enforcement. The bill faces an uphill climb in the Republican-backed U.S. House of Representatives.

Between 2000 and 2010, immigrants accounted for almost 40 percent of new homeowners, according to statistics from the White House.

Rebuild hardest-hit communities

Obama wants to address the uneven recovery in the housing market by rebuilding the communities hit hardest by the housing crisis. The goal is to employ more construction workers and to repair rundown homes and even tear down vacant properties.

The administration wants to use a program known as the Hardest Hit Fund to help in some of the areas devastated by foreclosures. The $7.6 billion fund, first unveiled in 2010 and paid for with leftover money from the 2008 federal bailout of the U.S. financial sector, is making slow progress. About $1.3 billion of that assistant program has been spent as of March.

Make rental housing more affordable

Besides ensuring that responsible borrowers who have the ability to buy a home can do so, the White House also wants to make sure that affordable rental properties are available to those who can't afford to buy.

Obama wants to create and preserve affordable rental housing for those who choose to not own a home by passing a bipartisan Senate proposal, officials said. He wants to push for more community-based assistance to help first-time home buyers get into vacant, foreclosed homes.

In the past, the U.S. has supported programs that allowed private investors to buy distressed homes in bulk and rent them out for profit. These investors often compete with first-time and lower-income buyers.

In his speech, Obama broadly spoke about the need for cities and states to work together to address local barriers that drive up rental housing costs for working families.

Reporting by Reuters' Margaret Chadbourn. NBC's Isolde Raftery contributed reporting.