ZAGREB (Reuters) - The Head of Croatia's conservative HDZ party, the biggest in a collapsed centre-right coalition, resigned on Tuesday after failing to form a new cabinet.

"I promised the party that I will be able to form a new parliamentary majority, which I failed to achieve," Tomislav Karamarko said.

The HDZ last week brought down technocrat Prime Minister Tihomir Oreskovic after falling out with him and a junior coalition partner over a conflict of interest case involving Karamarko.

Croatia is set to hold a snap election, probably in the first half of September, with the date to be set by Croatian President Kolinda Grabar-Kitarovic.

A recent opinion poll shows the HDZ trailing the main opposition party, the Social Democrats, for the first time since the previous election last November.

A Croatian member of the European Parliament, Andrej Plenkovic, has already announced his readiness to compete for the top post in the HDZ.

(Reporting by Igor Ilic; editing by Giles Elgood)