(Adds reaction by coalition partner)

BUDAPEST, June 14 (Reuters) - Hungary's Socialists have proposed a compromise deal to reform the health insurance system in a bid to resolve a conflict with their smaller coalition partner and avert a potential government crisis.

The Socialists and the junior coalition party, the economically liberal Free Democrats, have been at odds over the overhaul of the state health insurance system for months.

The Free Democrats, who welcomed the proposals, had wanted to open up health insurance to competition but the Socialists wanted less liberalisation, fearing that the poor and old, key voters for them, would lose out.

The Socialists proposed on Thursday that instead of one central state health fund there should be mandatory regional health insurance funds set up, in which private companies could invest and acquire a minority stake at a later phase.

These regional funds would be able to compete for clients.

"Healthcare needs therapy, but not shock therapy ... this is a wise and progressive compromise," Prime Minister Ferenc Gyurcsany told a news conference.

He said if the necessary laws were passed in parliament in the autumn, the new system may start from next year but that private firms would only be allowed in once the system was working in a stable way.

Gyurcsany said talks with the Free Democrats will continue and said he hoped a deal could be reached in one or two weeks.

Later on Thursday the Free Democrats said the new proposal meant significant progress in the health care debate as it would allow private capital into the system, a proposition which the Socialists initially firmly opposed.

"I'm glad that one year after the change in government the Socialist party came forth with a health care programme, even if it is primarily a political document," national news agency MTI quoted Free Democrat party leader Janos Koka as saying.

After years of overspending Gyurcsany's Socialist-led government, reelected for a second term in April 2006, launched a tough fiscal adjustment programme last year to cut the budget deficit which hit 9.2 percent of gross domestic product.

Overspending in health care and drug price subsidies had contributed to Hungary's massive deficit overshoots in the past.

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