PRAGUE (Reuters) - A plan to shake-up the Czech police to merge its anti-corruption units has split the centre-left coalition government and threatens to topple it more than a year before the election is due.

The European Union country's three-party government has ruled since 2014 despite squabbles between Prime Minister Bohuslav Sobotka's Social Democrats and Finance Minister Andrej Babis, a billionaire businessman and founder of the ANO party.

But a plan announced this week to create a national bureau by joining organised and economic crime units led to the resignation of the chief of the organised crime unit on Friday and angry exchanges among ministers in the media.

The plan was proposed by the police president and backed by Interior Minister Milan Chovanec, a Social Democrat.

Justice Minister Robert Pelikan, of ANO, has threatened to resign while Babis has not ruled out quitting the government and called the fight the coalition's most serious dispute to date.

State prosecutors oppose the move, saying it would impact open cases and raise the risk of evidence being leaked.

The Social Democrats say ANO is politicizing the issue and not respecting police independence.

"The re-organisation of the police is an expert matter that is under the competence of the police and interior minister. I reject any attempts by ANO to politicize and destabilise the work of the police," Sobotka said on Friday.

The parties will hold a coalition meeting next Wednesday.

The new bureau would be charged with tackling organised crime, corruption, terrorism, cybercrime and serious economic crimes.

Corruption in the political system has for years been top of the public agenda and attempts to tackle graft have had mixed results.

The organised crime unit has had some success but it has also been criticised for arresting an aide to then-prime minister Petr Necas - whom he later married - in 2013 on suspicions of graft, leading to the collapse of his cabinet.

Necas was later also charged in the case, but some of the allegations have been thrown out by courts and Necas has not been convicted of any crime to date.

The anti-corruption drive has been the main factor fuelling the popularity of Babis's ANO party, whose name means "Action of Dissatisfied Citizens".

His opponents say Babis, the biggest private employer in the country, should not be in politics because of a potential conflict of interest with his numerous business interests, spanning from farming and food processing to chemicals, fuels and the media.

Every cabinet in the Czech Republic since 2002 has either switched prime ministers or fallen apart during its term.

But thanks to low debt and strong institutions, the country maintains the best credit rating and lowest bond yields among central European neighbours.

(Reporting by Jason Hovet; Editing by Jan Lopatka and Janet Lawrence)