A Moldovan court has temporarily stripped pro-Russian President Igor Dodon of his duties, a move that has deepened an ongoing political crisis in the country.

The Constitutional Court appointed former prime minister Pavel Filip as interim president, who immediately signed a decree to hold a snap election in September.

However, parliament refused to accept, claiming the country's state institutions had been seized.

Filip's Democratic Party of Moldova had vowed to challenge the legitimacy of a new coalition government formed on Saturday by the Russian-backed Socialist party and the pro-European Union ACUM bloc.

The events worsened standoff between rival political parties over the formation of a new government after months of deadlock.

Maia Sandu, a former education minister and World Bank adviser, was appointed Prime Minister after Sandu's pro-EU bloc formed the coalition with the Socialist party. But a court struck down her appointment and that of a Socialist party-nominated parliament speaker.

The coalition broke months of deadlock after a February election resulted in a hung parliament.

Dodon is a former chief of the Socialist party and backed the formation of the new coalition government.

The EU's foreign policy chief Federica Mogherini and the EU's Commissioner for European Neighbourhood and Enlargement Negotiations Johannes Hahn said in a statement on Sunday that the EU stands "ready to work with the democratically legitimate government" and called for "calm and restraint".

An EU spokesperson confirmed that the "democratically legitimate government" was the coalition government and Sandu.

The Council of Europe's communications director tweeted that the Council of Europe calls on political forces to "act responsibly", stating that problems should be resolved by "the country's democratically elected representatives in Parliament."

Dodon called the move a "desperate step to take advantage of the controlled Constitutional Court in order to further usurp power" in a tweet on Sunday.

The court said Dodon had not followed a previous mandate that said parliament should be dissolved and another election held if a government was not formed by June 7.

Sandu is an opponent of the Democratic Party and accuses its leader Vladimir Plahotniuc of corruption and abuse of power.