By Michael Shields and Angelika Gruber

VIENNA (Reuters) - Austrian Finance Minister and Vice-Chancellor Michael Spindelegger unexpectedly quit all his political posts on Tuesday, citing lack of support from his conservative People's Party (OVP) in a row over tax reform.

His abrupt step comes amid a political battle raging in Europe over whether belt-tightening has gone too far at the expense of economic growth, a clash that also forced a government reshuffle in France this week.

Spindelegger also stepped down as OVP leader. But senior party members, and Social Democrat Chancellor Werner Faymann, said they expected their coalition, which squeaked out a thin majority in elections last year, to continue until the next national elections due in 2018.

Analysts said Spindelegger's exit could actually strengthen the coalition and increase prospects for stimulus measures by ushering in an OVP leader less keen on fiscal rigour.

Economy Minister Reinhold Mitterlehner, a pragmatist who has kept his head down in the tax battles, was seen as a likely candidate to succeed Spindelegger, while media speculated the OVP could split the roles of party leader and vice chancellor.

The OVP's most popular official by far is Foreign Minister Sebastian Kurz, but analysts say he may be too inexperienced - he turns 28 on Wednesday - to take the party helm, a post that the OVP could also hand to a regional OVP head.

Party chiefs were due to meet on Tuesday to pick a new head.

The OVP has been at loggerheads with its senior partner over how to finance income tax cuts to boost an economy that grew just 0.2 percent in the second quarter.

Spindelegger, who last year switched to finance from the foreign ministry, also faced an internal revolt over his refusal to cut taxes unless that can be financed without new levies.

"There has to be cohesion in a party. If the cohesion is no longer there, then the moment has come to hand over the tiller," he told a snap news conference to announce his resignation, showing no emotion and taking no questions from reporters.

WHO'S NEXT?

"What is surprising is the timing," political analyst Peter Filzmaier said. "No one could imagine that he would be the top candidate in the next parliamentary elections with chances to become chancellor. But ... you don't do this at the start of provincial elections in Vorarlberg in four weeks."

The OVP may lose its absolute majority in that western province, and four more state elections are due next year. The OVP's popularity has fallen below 20 percent in opinion polls as the far-right Freedom Party gains.

That posed problems for Spindelegger, a 54-year-old lawyer from Lower Austria who filled an OVP leadership vacuum in 2011 when his predecessor quit due to ill health.

Faymann, responding to questions at a news conference about the durability of the government coalition after Spindelegger's resignation, said: "I expect it will hold until 2018."

Faymann underscored the need to cut taxes - tax rates start at 36.5 percent for income over 11,000 euros - by mid-2015. "I will do my utmost to meet this timetable," he said, adding savings and additional revenue were needed to finance this.

He wants a tax on millionaires to help raise revenue, an idea that was anathema to Spindelegger.

Regional OVP leaders have been grumbling aloud about Spindelegger's leadership for weeks, and the rebellion broke into the open on Tuesday when OVP member and Tyrol Chamber of Labour head Erwin Zangerl called for Spindelegger to go.

"The OVP needs someone who represents the people, not the lobbyists," Zangerl told the Oesterreich tabloid. "He has given enough proof that he no longer understands the people. He is deaf in both ears."

TOWARDS BERLIN, NOT ATHENS

Spindelegger to the last refused to go along with calls for immediate tax cuts at a time of record high state debt.

"Now a situation has arisen where a clear signal is coming from my own party. People who say we have to jump on the populist bandwagon are winning the upper hand," he said.

Wolfgang Bachmayer, head of market research institute OGM, said Spindelegger's exit when party bigwigs failed to back him publicly had improved prospects for a stimulus deal.

"Faymann will have a few fewer problems now. The governing coalition will be strengthened because consensus will be found on these issues," he said.

(Additional reporting by Georgina Prodhan, Alexandra Schwarz-Goerlich and Shadia Nasralla)