PRAGUE (Reuters) - Czech President Milos Zeman on Monday demanded his prime minister terminate the agreement that formed the coalition government if he is to agree to firing the finance minister, deepening a rift between the country’s two leaders.

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The European Union member is in political crisis over the future of Finance Minister Andrej Babis, a billionaire businessman who faces questions over past business practices and is the main political rival of Prime Minister Bohuslav Sobotka.

With an election due in October, Sobotka is demanding the president dismiss Babis, but the finance minister, who heads the anti-establishment ANO party, has found an ally in Zeman who has long had poor relations with the prime minister.

Sobotka, who heads the centre-left Social Democrats, asked Zeman on Friday to dismiss Babis by May 9, but the president has refused to do so.

“The president stated that the prime minister cannot task the president with setting a date for dismissal,” the presidency said in a statement issued after Zeman met Babis on Monday.

Under the constitution, the president dismisses a minister if requested by the prime minister. Lawyers say the head of state should act promptly and has little wiggle room.

However, on Monday Zeman said Sobotka’s and Babis’s parties were bound by coalition agreement -- reached in 2014 to form the cabinet -- and that the prime minister must pull out of the deal before requesting Babis’ dismissal against the minister’s will.

“A termination of the coalition agreement would be needed for a valid dismissal,” the statement said.

Such a move could trigger the coalition government’s collapse. Last Friday the prime minister took back a pledge to resign along with his whole government in order to dislodge Babis.

Zeman also wanted to see a nomination for a replacement, the statement added.

Sobotka later urged the Zeman to respect the constitution.

“I would like to call on Mr President to respect the fundamental law of our country. The coalition agreement has nothing to do with that,” the prime minister said in a statement.

Sobotka has said Babis failed to clear suspicions he dodged taxes by buying tax-free bonds from his conglomerate Agrofert. Babis says he has not violated any laws.

The EU’s fraud office and Czech police have also been investigating whether Babis manipulated ownership of a conference center to unfairly qualify for EU subsidies meant for small businesses.

Babis has said the prime minister’s actions are politically motivated ahead of parliamentary elections in October. Babis’ ANO party enjoys a more-than 10 point lead over the Social Democrats, according to opinion polls.