ZAGREB (Reuters) -Croatian Prime Minister Andrej Plenkovic said on Thursday his long-dominant ruling HDZ party will announce the name of a coalition partner "very soon", after it won Wednesday's snap election but fell short of an outright majority.

With nearly all votes counted, the conservative HDZ (Croatian Democratic Union) won 61 seats in the EU member state's 151-seat parliament, five fewer than the last election and 15 short of a majority, according to preliminary results.

"We spoke with some colleagues already on the very night of the election. We are continuing the talks today," Plenkovic said on his party's Facebook page.

"Very soon you will find out with whom we will form the new majority."

Final results are not expected until next week because a re-run is needed in two polling stations after irregularities were recorded, election commission head Radovan Dobronic said in a press conference on Thursday.

A coalition led by the opposition Social Democratic Party (SDP) came in second with 42 seats, a poorer result than expected after President Zoran Milanovic dissolved parliament in March and triggered a surprise election in which he said he would run for the SDP to become prime minister.

The far-right Homeland Movement took third place with 14 seats, potentially giving it a decisive role in getting the HDZ over the line.

But talks will be tough - Homeland has pledged not to join either main bloc and has reservations about other smaller parties.

The nationalist party said it will not join any government that includes the Serb minority party SDSS. A coalition with the leftist green Mozemo party is a "mission impossible", Homeland Movement head Ivan Penava said.

Still, he left the door ajar: "I hope that we shall tailor the fate of Croatia in the days ahead," Penava added.

Other opposition parties, including Mozemo and Most which won 10 and 11 seats respectively, called on all parties to unite against the HDZ.

In the last parliament, the HDZ held a majority through support from SDSS and other smaller parties.

OLD RIVALRY

The HDZ, which has dominated Croatian politics since Socialist Yugoslavia broke up in 1991, took credit for the country entering the EU's Schengen free travel area and the Eurozone last year.

It has also overseen a boom in tourism to Croatia's old walled cities and rugged coastline. But many ordinary citizens feel tired by corruption scandals and economic hardship. The party denies allegations of graft.

The short election campaign was marked by rivalry between Prime Minister Plenkovic and President Milanovic, who disagree over the conflict in Ukraine, relations with the European Union and other issues.

Pro-EU Plenkovic is in favour of helping Ukraine; Milanovic is not.

Citizens of the capital Zagreb appeared mainly disappointed by the results on Thursday.

"I expect it will be even worse. It won´t be better for sure," a man named Leo said. His monthly 400-euro pension did not even cover basic costs, he added.

"Those who say they are fine, ok, let them dig through the trash, these are the people that mainly voted."

(Reporting by Fedja Grulovic, Daria Sito-Sucic and Aleksandar Vasovic, writing by Daria Sito-Sucic; Editing by Philippa Fletcher, Edward McAllister and Andrew Heavens)