By Robert Muller and Jan Lopatka

BRNO, Czech Republic (Reuters) - Czech Prime Minister Petr Necas won re-election as head of the center-right Civic Democrats on Sunday and must quickly tackle a rebellion among the party's backbenchers that could bring down his cabinet next week.

The leadership challenge came from one of a group of dissenters who oppose Necas's plans to hike taxes next year. The rebels could still bring down the prime minister in a confidence motion tied to the tax bill and due for a vote on Wednesday.

The center-right cabinet has won praise from investors over its two years in office for a determined push to narrow the budget deficit. But that has come at the cost of squeezing domestic demand and prolonging a recession that has strangled the economy since late last year.

If Necas were to fall next week, he would join a string of prime ministers from the Netherlands to Romania brought down over austerity measures in recent months.

Necas rallied the party to support the tax hike.

"If the government loses support for its budget policy, it will lose the purpose for its rule," Necas told 600 delegates at the party's congress in Brno, 200 km southeast of Prague.

"We should not square over 1 percentage point in one tax rate for one year when the alternative is opening the way to the left, which has already said it wants to raise taxes by 3 percentage points of GDP," he said.

Necas plans to increase value-added, income and other taxes to raise extra 22 billion crowns ($1.12 billion) to cut the budget gap under the EU's ceiling of 3 percent of gross domestic product next year. As a concession to win over more support, he has offered to reduce some of the increases.

Necas's coalition has lost its safe majority and now has 99 seats in the 200-seat lower house, including a handful of the anti-tax dissenters.

He may still win support from some independent deputies or members of a former coalition party that split from the cabinet earlier this year, but the result remains uncertain.

Necas refused to say after the vote how he would secure enough votes for the tax legislation.

The prime minister was challenged by Ivan Fuksa, one of the dissenters, for the party chairmanship. Fuksa, who lost by a margin of 351 to 178, said he was ready for further talks to find a deal on the taxes.

"Our aim is not a fall of the cabinet, no early election, but we are saying no to tax increases, and I believe we will hold more negotiations and reach a compromise," he said.

Necas has said that if he fell an early election should be held, although that is not mandatory under Czech law.

A steep drop in popularity for the ruling parties, including the conservative TOP09 and the small centrist LIDEM party, could force them to try to find a new prime minister to hold on to power until regular elections due in 2014.

The center-left opposition Social Democrats hold a double-digit lead in opinion polls over the Civic Democrats and are demanding elections be held as soon as possible.

The Social Democrats favor slapping higher taxes on big companies and top earners to help narrow the budget gap, and rolling back reforms in the health sector including the introduction of fees for doctor visits and some procedures.

($1 = 19.6609 Czech crowns)

(Editing by Hugh Lawson)