By Lefteris Papadimas

ATHENS (Reuters) -Greece's president will appoint a caretaker prime minister on Wednesday to form a government that will lead the country to a repeat election on June 25, after last weekend's inconclusive vote.

The conservative New Democracy party of Prime Minister Kyriakos Mitsotakis stormed to victory polling 40.1% last Sunday, but fell short of an outright majority. The country's top three parties, including New Democracy, have turned down a mandate for a governing coalition, pushing for a second vote on June 25.

Mitsotakis believes a second vote, which gives the leading party bonus seats, will give New Democracy the majority needed to rule alone.

Opposition parties also declined separate offers to seek a coalition after failing to secure the necessary number of seats in the 300-seat legislature. They hope a second vote will boost their ratings.

On Wednesday, the president invited the leaders of all the parties whose share of votes surpassed the threshold of 3% to discuss steps forward. The invitation was procedural, and the brief talks did not produce a coalition government.

Under Greece's constitution, if coalition talks fail, the president appoints a caretaker prime minister to lead the country to a repeat vote.

The task will be handed to Ioannis Sarmas, a senior judicial official who is president of the Council of State, one of the country's three senior courts.

The leader of the Communist KKE party Dimitris Koutsoumbas said a repeat election would be held on June 25.

"We are led to a caretaker government, with elections on June 25 and there we will give battle," Koutsoumbas told state ERT TV.

Under Greece's electoral system, the winner of a second vote following an inconclusive first election can receive up to 50 bonus seats for every point it wins beyond 25%.

To benefit from bonus seats, New Democracy needs to stay the biggest party, but that seems likely as its nearest rival, Syriza, secured just a fifth of the votes on May 21. If it secures 40% of the vote again or even a little less, it will most likely have a clear majority.

The total seats New Democracy secures will, however, depends on how many other parties make it into parliament.

The new parliament which emerged from the May 21 election will convene next Sunday and be dissolved a day later before the caretaker government takes over.

(Additional reporting by Renee Maltezou; Editing by Clarence Fernandez and Bernadette Baum)