(Adds analyst, former minister, Socialist MP)

By Krisztina Than

BUDAPEST, April 5 (Reuters) - The resignation of Hungary's health minister means a decision on legislation to introduce private insurance into healthcare will be delayed beyond the planned April date.

The Socialists, the largest party in the ruling coalition, want to slow changes to health insurance, fearing a market-based model in which there are multiple private insurers would mean their older, poorer voters will suffer.

The Free Democrats, a smaller, economically liberal party with 20 seats in parliament of the 210 held by the government, wants the multiple model so as to reduce costs for the state.

It was their health minister, Lajos Molnar, one of three Free Democrat ministers, who resigned on Wednesday.

"The essence of health reform is the introduction of a multiple insurer system ... and I trust we will convince the coalition partner that the multiple insurer model is better," party leader Janos Koka said on Thursday.

Koka said his party would finalise an agreement with the Socialists about the multiple insurer model within six weeks as the new system should start working in January 2008.

Reforming Hungary's costly health system is a key element in putting the budget deficit, which was the largest in the European Union in 2006 at 10 percent of gross domestic product, on a sustainable path in the longer term.

Molnar said in a statement on Thursday that he stepped down as he could not accept any further delay in the decision about transforming the insurance system.

However, senior Socialist officials remained sceptical and say firms would be able to cherry-pick the best clients.

Government spokesman and Socialist member of parliament Zoltan Gal said discussions would last for months. Other Socialists voiced deep disquiet with the Free Democrat plans.

"Where there is a pure business based-insurance, they leave the costly services to the state, do not accept patients with high risk factors and ... also the poor can fall out," Tibor Schvarcz, head of the Socialist MPs health group told Reuters.

Political analysts say the disagreement is unlikely to bring down the coalition. Koka won his party's presidency on Saturday and is struggling with poll ratings which show the party would not make it into parliament if elections were held now.

"The issue will definitely not blow up the government... First they will have a juicy quarrel and then they will announce a solution together," said Zoltan Kiszelly, political analyst at the Hungarian Academy of Sciences.

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