Croatia's ruling conservative party has reached a deal with a right-wing party to form a new coalition government following last month's vote, a spokesman said on Wednesday.

The alliance is set to shift the country to the right again, after pro-European incumbent Prime Minister Andrej Plenkovic moved the governing Croatian Democratic Union (HDZ) towards the centre.

Plenkovic's HDZ and a centre-left coalition led by the Social Democrats (SDP) have been scrambling to form a governing coalition since April's elections.

But Marko Milic said that the HDZ -- the main governing party since independence in 1991 -- and the nationalist right-wing Homeland Movement (DP) have now "reached an agreement on the formation of a new parliamentary majority and structure of a new government".

The new government will be led by Plenkovic, who has held the office in the Balkan nation since 2016.

The DP, known for its nationalist and anti-migrant rhetoric, insisted on a set of provisions including barring the main ethnic Serb party -- the SDSS -- from the coalition.

The SDSS was traditionally Plenkovic's ally, and had a vice prime minister from its ranks.

In the April 17 parliamentary election, no party won an outright majority in the 151-seat assembly.

The HDZ won 61 seats while the DP secured 14.

Plenkovic is also expected to get support from some of eight other MPs representing minorities.

Under the Croatian system, the president names a prime minister-designate, backed by a majority of MPs, who is then voted on by the full parliament.

The newly elected parliament's inaugural session must be held by May 19.

The April vote was held after a bitter campaign between the country's longtime political foes -- Plenkovic and left-wing populist President Zoran Milanovic.

Milanovic, who topped popularity surveys, made the shock announcement in March that he would challenge Plenkovic.

However, Croatia's top court last month barred Milanovic from heading the new government.

The elections were held as the European Union nation of 3.8 million people struggles with challenges including corruption, a labour shortage, the highest inflation rate in the eurozone, and undocumented migration.