The Free Democrats, who have 20 seats in parliament compared with 190 for the Socialists, had said on Monday that they would resign on April 30 after Gyurcsany sacked their health minister and watered down reforms which were their main policy goal.
After the meeting with Gyurcsany on Tuesday, Peter Gusztos, a member of the party's presidency, said: "If there is a minority government, the Free Democrats will support all decisions which serve meeting the objectives of the (euro) convergence programme... and the interests of structural reforms."
Earlier, Gyurcsany had asked both the Socialists and Free Democrats in an open letter to reaffirm their commitment to cutting Hungary's budget deficit.
Hungary has a record of heavy pre-election spending and keeping to proposed budget cuts is vital to retaining the confidence of investors who hold billions of dollars of Hungarian bonds.
Gyurcsany spent heavily to win re-election in 2006 and the country's budget deficit hit 9.2 per cent of gross domestic product (GDP) in that year, but since then hefty tax rises and cuts in subsidies have reduced the deficit.
Hungary has promised the European Union that the deficit will fall to 3.2 per cent of GDP in 2009, a year ahead of elections, and close to the level needed for euro membership.
It had been reported that Gyurcsany had offered to resign at a Socialist Party meeting after the leader of the Free Democrats said he might reconsider the decision to quit the coalition, but that the offer had been rejected.
However, Ildiko Lendvai, a member of the Socialist Party, denied that Gyurcsany had offered to resign and said her party was committed to the reform process.
Ratings agency Standard & Poor's, which cut its outlook on Hungary's debt to negative earlier this month, has said that prospects for the country's finances were worsening and that it saw no chance of economic reforms being pushed through.
Frank Gill, an S&P analyst, said: "We just do not see much support in the political system (for reform) on the spending side."