Soon after Godmanis quit, the largest party in the old coalition, the People's Party, and the second largest opposition party, New Era, said they were ready to work together in government, the Baltic news agency BNS reported.
Latvia has seen its economy boom in the last few years, the country achieved that fastest economic growth in the EU in 2006, but the country has been badly hit by the global credit crunch.
The Baltic state slipped into recession in 2008 and had to take a $9.43bn loan from the International Monetary Fund (IMF) and other lenders in December.
As part of the deal, the government cut public spending and increased taxes.
IMF officials were visiting Latvia for follow-up talks when Godmanis quit.
Latvia's economy is expected to shrink 12 per cent this year, with unemployment soaring to 12.7 per cent from the current 8.3 per cent.
Lars Christensen, chief analyst at Danske Bank, said that "the renewed political crisis in Latvia is likely to deal yet another blow to the already hard-hit Baltic markets".
Christensen also warned that, if Latvia called elections, there could be "a rise in populist sentiment and it is very likely that the government's austerity measures will come under serious criticism".
The government's belt-tightening, along with allegations of corruption, sparked riots in January, when about 10,000 people rallied in Riga, the capital, and hundreds of protesters clashed with security forces.
Recent polls suggest that opposition parties would win an election.
Latvia has had 14 governments since the Soviet Union collapsed in 1991 and its politics often see the same parties falling in and out of coalitions.
Godmanis, from the small Latvia's First/Latvia's Way party, led the country to independence as prime minister in 1990-1993.
He took office in December 2007 when Aigars Kalvitis, of the People's Party, quit following street protests over alleged abuse of power and economic mismanagement.