Support at the Socialist Party meeting does not guarantee all its parliamentarians will vote in favour of the bill. Regional representatives of Gyurcsany's Socialist Party voted unanimously to back the bill which would allow private investment in health insurance and is key to Gyurcsany's efforts to cut Hungary's budget deficit to adopt the euro.
The plan to overhaul the costly health system of the former communist state has been criticised by senior Socialist politicians and was agreed after months of argument with the smaller coalition party, the liberal Alliance of Free Democrats.
"If such a bill fails it naturally presents a completely new situation for a government because one of its most important objectives is not achieved," Gyurcsany told a news conference.
Support at the Socialist Party meeting does not guarantee all its parliamentarians will vote in favour of the bill.
"I am very confident that on Monday parliament will pass the law on health funds," Gyurcsany said. The coalition has a majority in parliament of about 40.
Later on Saturday Socialist caucus leader Ildiko Lendvai said the group supported the bill and had accepted an opposition request for a named vote instead of a secret ballot to show each MP's stance.
The legislation would keep the state health insurer but set up 22 health funds and allow private firms to buy minority stakes in the funds to encourage competition and try to boost the health sector's efficiency.
Socialist deputies, scared of defeat in a 2010 parliamentary election, want to slow any further reforms. The Free Democrats want reforms to continue.
Several trade unions plan to start strikes on Monday to protest against the bill they fear will disadvantage poor people. About 1,000 people held a demonstration outside parliament on Saturday.
On Tuesday, coalition parliamentarians backed amendments to the bill proposed by the government, which Gyurcsany said could lead to private investment of 100 billion forints ($570 million) in health care.
Gyurcsany, who survived months of violent anti-government protests last year, has been criticised by Socialists for running a "one-man show" and not doing enough to shore up the party's popularity.
However, he has won praise from foreign investors for his tough programme to cut the budget deficit which last year hit 9.2 percent of gross domestic product.
Tax hikes and subsidy cuts have sent the Socialists' ratings to historic lows, around 13-16 percent in the latest opinion polls.
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