President Barack Obama announced an 11th-hour deal with Congress to avert an unprecedented default on US debt payments, triggering a widespread rally on stock markets Monday and sighs of relief around the world.

With just two days left before the United States would run short of cash, Obama and his Republican foes said late Sunday after round-the-clock negotiations that they had reached a framework for more than $2.4 trillion in spending cuts.

"I want to announce that the leaders of both parties in both chambers have reached an agreement that will reduce the deficit and avoid default, a default that would have had a devastating effect on our economy," Obama said.

"This process has been messy; it's taken far too long," Obama told a hastily convened evening press conference. "Nevertheless, ultimately, the leaders of both parties have found their way toward compromise."

But the package still needs approval from Congress, which could vote as early as Monday. Leaders of the Democratic-held Senate and Republican-led House of Representatives were working to rally polarized lawmakers.

"To pass this settlement, we'll need the support of Democrats and Republicans in both the House and Senate. There is no way either party -- in either chamber -- can do this alone," said Democratic Senate Majority Leader Harry Reid.

House Speaker John Boehner called the plan a remedy to avert "a job-killing national default that none of us wanted."

But the plan faces opposition both from the conservative "Tea Party" movement, which favors sweeping spending cuts, and liberal Democrats who want taxes on the wealthy before any thought of cutting social welfare programs.

As described by Obama and congressional leaders, the deal would raise the country's $14.3 trillion debt ceiling by at least $2.1 trillion. It would also make more than $2.4 trillion in spending cuts in two steps, including through a special new committee required to submit proposals by November 23.

Asian and European stock markets cheered the deal. Tokyo closed 1.34 percent higher, Sydney gained 1.65 percent and Seoul rose 1.83 percent while Hong Kong was up 1.53 percent by the break. The dollar also strengthened against the yen.

In early morning trading, London's benchmark FTSE 100 index climbed 1.08 percent to 5,877.97 points, Frankfurt's DAX 30 grew 0.61 percent to 7,203.64 points and in Paris the CAC 40 gained 0.80 percent to 3,701.13.

Japanese Chief Cabinet Secretary Yukio Edano said he expected the agreement will "lead to the stabilization of markets."

French Finance Minister Francois Baroin, for his part, noted that the latest developments -- the eurozone agreement on Greece and the deal in Washington -- were moves "in the right direction ... of reinforcing global growth."

In Washington, Republicans crowed that the framework did not explicitly call for raising tax revenues -- at least in the first wave of deficit cuts -- despite Obama's repeated calls for increasing revenues from the rich and wealthy corporations.

The framework would also fulfill one of Obama's top goals: Giving cash-strapped Washington the ability to borrow by enough to avoid another politically fraught debt battle before he faces re-election in November 2012.

The package would cut military spending by at least $350 billion at a time that the United States is looking to exit Iraq and Afghanistan. A White House official hoped half of total cuts would come from defense, but leading Republicans have already cried foul.

Obama trumpeted that the cuts would bring annual domestic government spending to the lowest level in 60 years but promised they would not come so "abruptly" as to be a "drag" on the fragile US economy, still struggling with stalled growth and 9.2 percent unemployment in the wake of the 2008 meltdown.

But Representative Raul Grijalva, a fellow Democrat and co-chair of the Congressional Progressive Caucus, rejected the framework in a blistering statement declaring: "This deal is a cure as bad as the disease. I reject it."

Democratic House Minority Leader Nancy Pelosi, who planned to present the framework to her rank-and-file on Monday, said "we all agree that our nation cannot default" but gave Obama's announcement a chilly welcome.

"I look forward to reviewing the legislation with my caucus to see what level of support we can provide," said Pelosi, who lost her job as House speaker when the Republicans stomped to victory in November elections.

The New York Times was sharply critical in an editorial, saying that the deal was "a nearly complete capitulation to the hostage-taking demands of Republican extremists."

Tea Party lawmakers who triumphed in November have pushed for dramatic spending cuts and put strong pressure on Boehner. Tea Party favorite Representative Michele Bachmann quickly voiced opposition to the package.

"The 'deal' he announced spends too much and doesn't cut enough," Bachmann, a Republican presidential candidate, said of Obama. "Someone has to say no. I will."

It was unclear whether the accord would be enough to placate ratings agencies that have warned Washington's sterling Triple-A debt rating was in jeopardy -- a downgrade that would lead to a painful spike in interest rates.

Leading asset manager BlackRock said in a statement it was "encouraged by momentum to raise US debt ceiling, but believes investors need to see real deficit reduction without delay."