"Following the second round of local elections (on 2 June), I will ask the president to immediately call national elections", Tsipras said in a televised address Sunday, cited by AFP.
Earlier on Sunday, the leader of Greece's opposition New Democracy party which is leading in the European Parliament elections, Kyriakos Mitsotakis, called for the resignation of Alexis Tsipras.
"The prime minister must take responsibility and he must resign, and the country will head to national elections as soon as possible", Mitsotakis said.
The liberal-conservative New Democracy party is gaining 33.07 percent of the vote and is currently ahead of the ruling Syriza party, which is headed by Tsipras, by 9 points, according to preliminary results, released by the country's Interior Ministry on Sunday.
From 7 a.m. to 7 p.m. (04.00-16.00 GMT), more than 39,000 polling places were open across Greece. The Greeks elected 21 members of the European Parliament, heads of 13 regions and 332 municipalities, 703 regional councillors and almost 10,000 municipal councillors.
European parliamentarians are elected for five years while local authorities are chosen for four. Forty parties and electoral blocs have been admitted to the elections, with the main competitors the ruling SYRIZA party (the Coalition of Radical Left) led by Prime Minister Alexis Tsipras and the conservative New Democracy led by Kyriakos Mitsotakis.
There are 1,200 candidates for the country's 21 seats in the European Parliament or 57 people per seat. Almost 7,700 candidates are on the lists for regional councillors elections, and 69,800 for municipal councillors.