U.S. stock indexes fell more than 1.5 percent after rallying strongly this month.

"It's the move down in stocks and also one of those 'Who's next?' trades prompted by the MF Global bankruptcy filing," said Cary Leahey, managing director and senior economist at Decision Economics in New York. "But it's also because, after a phenomenal month, investors can't help but have second thoughts on the last day of the month, particularly given what little transpired last week in Europe."

MF Global Holdings, also a primary dealer run by former Goldman Sachs chief Jon Corzine, filed for Chapter 11 bankruptcy after a tentative deal with a buyer fell through. The New York Federal Reserve suspended the firm from conducting new business with the central bank.

Appetite for safe-haven U.S. debt was whetted by more than the troubles of one firm, however.

"You had the continued deterioration of the outlook for the European situation, you have equities trading off, and you also have a fairly large month-end buying program going through," said Scott Graham, head of government bond trading at BMO Capital Markets in Chicago.

Benchmark 10-year Treasury notes traded 1-19/32 higher in price Monday to yield 2.13 percent, down from 2.32 percent late Friday.

While benchmark notes were on track for the best single-day performance since early August in the wake of Standard & Poor's downgrade of the U.S. credit rating, the notes were also set for the worst monthly performance since December 2010.

Worries about Europe bolstered the safe-haven allure of U.S. government debt.

European policymakers "made stabs in all the right directions, dealing with Greece, bank solvency and the larger question of contagion," said Leahey. "But a lot of detail remains to be filled in and the time frame for recapitalizing European banks is surprisingly slow."

Compounding the implementation issues "is the basic problem of how to achieve the stronger growth needed to service debt when everybody is tightening their belts," Leahey said.

"In the past when small economies have done what we'd all love Greece to do, they did it against a much stronger global and European economic backdrop," Leahey said.

Thirty-year Treasury bonds Monday traded 4-27/32 higher in price, with their yields plummeting to 3.14 percent from 3.37 percent late Friday. The bonds were on track for the best single-day performance since March 18, 2009, when the Federal Reserve announced its first round of quantitative easing under which it bought $300 billion of Treasuries in an effort to stimulate the economy.

Bonds were also set for the biggest monthly rise in yield since January.

The safety bid that drove U.S. Treasuries prices higher Monday also lifted safe-haven German government bonds as peripheral eo zone debt came under pressure.

Japan sold the yen for the second time in less than three months after it hit another record high against the dollar, saying it intervened to counter speculative moves that were hurting the economy.

In Vienna, Chinese President Hu Jintao said Europe had the capacity to overcome its economic problems, but offered no indication as to whether Beijing could play a major role in helping solve the euro zone's debt crisis.

A two-day Federal Reserve policy meeting begins Tuesday, with Fed officials worried about the U.S. economy's health and looking at ways to offer more monetary stimulus -- including helping the distressed housing market.