By Krisztina Than BUDAPEST, April 5 (Reuters) - The resignation of Hungary's health minister on Wednesday means that 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 that 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. However, senior Socialist officials remained sceptical, saying firms would be able to cherry-pick the best clients. Government spokesman and Socialist member of parliament Zoltan Gal said on Thursday there was agreement that the system had to be changed and that competition was needed. But he said discussions about the best model would last for months. Political analysts say the disagreement is unlikely to bring down the coalition, although the main centre-right Fidesz opposition has scored a victory with Molnar's resignation. 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.