In late afternoon trading in New York, the Dow Jones Industrial Average gained 0.97 per cent, the Standard & Poor's 500 Index rose 0.60 per cent and the Nasdaq Composite Index advanced 0.76 per cent.
In Europe, the Stoxx 600 Index ended the day with a 0.6 per cent advance, reversing losses earlier in the session. Shares closed higher in London, Frankfurt and Paris.
"The daily egg shells we walk on this week over Spain will, of course, be followed by Sunday's election in Greece and what, if anything, the FOMC will announce next week," Peter Boockvar, equity strategist at Miller Tabak & Co in New York, told Reuters.
The optimism for central bank assistance lowered the appeal of US Treasuries in today's auction of US$32 billion of three-year notes.
The securities drew a yield of 0.387 per cent, compared with a forecast of 0.383 per cent in a Bloomberg News survey of seven of the Federal Reserve's 21 primary dealers.
"The auction was good, but not great," Michael Franzese, managing director and head of Treasury trading at Wunderlich Securities in New York, told Bloomberg. "They had buyer's fatigue. You have a marketplace where yields are close to their lows and it's possible Europe may get their act together."
The Treasury plans to auction US$21 billion of 10-year bonds on Wednesday and US$13 billion of 30-year debt on Friday.
Meanwhile, Austrian Finance Minister Maria Fekter on Monday warned that Italy will be next in line for outside financial assistance. "Italy has to work its way out of its economic dilemma of very high deficits and debt, but of course it may be that, given the high rates Italy pays to refinance on markets, they too will need support," Fekter said in a TV interview.
On Tuesday she tried to play down her remarks, saying she had no indication Italy planned to apply for aid.
Earlier today Spain saw its 10-year yield climb to 6.83 per cent, a record since the introduction of the euro in 1999, before easing back.