* PM ready to quit to enable reforms, budget cuts
* Source says aim is to have new PM, govt by mid-April
* Finding backing for new PM, programme could be hard
* Main opposition party Fidesz wants early election
(Recasts with Free Democrats, Fidesz, congress, analysts)
By Krisztina Than and Gergely Szakacs
BUDAPEST, March 21 (Reuters) - Hungarian Prime Minister Ferenc Gyurcsany offered on Saturday to step aside to allow a new leader and government to tackle the ailing economy, but finding a compromise candidate and programme may be difficult.
Hungary, which had to resort to an IMF-led rescue package last October, needs to make further spending cuts and other measures, but the ruling Socialist minority government has so far been reluctant to agree to bold cuts in social spending.
Gyurcsany, in power since Sept. 2004, told the Socialist's party congress he would stop leading the government if this was needed to lead the country out of its troubles.
The liberal Free Democrats, with whom the Socialists will most likely have to agree on a new leader and programme, want radical tax and spending cuts.
Should Gyurcsany no longer be prime minister, he would still wield considerable political influence as leader of the Socialists, the largest party in parliament.
"Crisis management and further changes require wider political and social backing than today," he said.
"I hear that I am the obstacle to the cooperation required for changes, for a stable governing majority and the responsible behaviour of the opposition," Gyurcsany said "...If so, then I am eliminating this obstacle now. I propose that we form a new government under a new prime minister."
A source close to Gyurcsany told Reuters he planned to organise a parliamentary vote of no confidence against him and his government. In the same vote, parliament would also vote on a new prime minister, avoiding the need for elections.
"In a legal sense this will not be a resignation, but a constructive vote of no confidence, headed by the PM," the source said. "If there is a parliamentary majority, there could be a new prime minister by mid-April," he said.
Gyurcsany was re-elected as party president with 85 percent support at the congress later on Saturday. The Socialists plan to choose their candidate for the premiership on April 5.
To get the new leader and programme approved in parliament, the Socialists need the backing of opposition MPs, primarily from the Free Democrats.
"If there is a turn to the left at the Socialist Party's (ongoing) congress, the chance will pass to cooperate about sensible reform policies," Gabor Fodor, party chairman of the liberal Free Democrats told a news conference.
The main opposition party Fidesz said it would not negotiate about a new government and would on Monday submit a motion to dissolve parliament as it wants early elections.
DIFFICULT COMPROMISE
Gyurcsany has headed a minority Socialist government since last April when the Free Democrats quit the coalition and a compromise prime minister able to get majority support in parliament could be hard to find, analysts said.
"The most important question of the vote of no confidence procedure and the establishment of a new government is not so much the person of the new prime minister but the programme which can attract majority support in parliament," think tank Political Capital said in a note. [ID:nLL418191]
"It may not be simple to find a compromise over the programme," added Zoltan Kiszelly, another analyst.
The global financial crisis has hit Hungary hard and in October it took a $25.1 billion IMF-led rescue package.
Hungary's export-dependent economy is expected to contract by 4.5 percent this year and some analysts say the recession could be deeper. The national debt is rising and the currency fell to record lows against the euro earlier this month.
In 2006 Gyurcsany's re-election to power sparked weeks of riots after a tape in which he admitted lying about the country's poor finances to win the election.
Although Gyurcsany cut the deficit from more than 9 percent of GDP in 2006 to 3.3 percent in 2008, he has failed to win public support for wider economic reforms and his popularity has plunged to record lows because of tax rises and spending cuts. (Writing by Krisztina Than, Editing by Matthew Jones)