The decision on setting the election convention for 2 June was made at a session of the SDP Main Committee in Zagreb on Saturday.
During the session, only Zoran Milanovic announced his candidacy for president of the strongest opposition party.
After the session, which was held behind closed doors, the acting president of the party, Zeljka Antunovic, and the Main Committee chairman, Tonino Picula, did not want to say explicitly whether they would also run for the post previously held by Ivica Racan, who recently resigned and who is being treated for cancer.
Picula told the press he believed that the party would nominate him for the post of party president.
Antunovic said that she would announce her decision when she assessed that this should be done.
"I will inform the public about it when I decide that it is necessary and possible," Antunovic said.
She added that her possible candidacy would depend on "whether the SDP will show responsibility and a true wish to win the (parliamentary) elections".
Both Picula and Antunovic told the press conference that the situation with their candidacies would be clearer in the coming days.
Addressing reporters separately, Zoran Milanovic, a member of the party's Executive Committee, said his candidacy for party leader was a new democratic step forward made by the SDP.
After the Main Committee's session, Milanovic told the press that "this is yet another democratic step forward in a party that has been the most democratic party so far".
He added that he would like to bring new energy into the SDP.
Asked to describe himself as a prospective SDP leader, he said that he perceived himself as a leader of a team and a programme that had already been defined to a large extent and that offered the SDP a great opportunity of winning the parliamentary elections.
Asked whether Racan was referring to him when he wrote in his letter of resignation that he wished the SDP new strength, Milanovic answered that what Racan was thinking when he wrote that would remain secret.
Milanovic added that he believed that Racan was not referring to individuals, but to the whole party.
Asked whether he also had ambitions to become the SDP's candidate for prime minister, Milanovic said he considered the post of SDP leader and the candidacy for the post of prime minister two separate things.
He refuted media allegations that he had made a deal with Ljubo Jurcic that he (Milanovic) run for the post of party leader and that Jurcic be the party's candidate for prime minister.
"There was no deal. The only deal is to ensure the SDP's victory in the elections," said Milanovic.
Antunovic told the press conference that the SDP had not discussed today the question of the SDP's candidate for premiership.
Both Antunovic and Picula voiced satisfaction with the party's unity, which they said was proved at today's meeting.
Asked by reporters to comment on Milanovic's candidacy, she said she had always approved of people showing their ambitions.
Commenting on Jurcic's wish to be the SDP's candidate for the country's premier, Antunovic said that Jurcic's statements should be interpreted as "a clear and unequivocal expression of ambitions and not of the candidacy".
She added that ambitions were not the only criterion for deciding on the matter.