The meetings on Sunday followed three days of street clashes in the capital, Dhaka, and other towns and cities that left 19 people dead and hundreds injured.
Iajuddin Ahmed first intervened on Saturday, the day the prime minister's five-year mandate expired and KM Hasan, the former supreme court chief justice, was to have taken charge of an interim administration to prepare for national elections.
With opposition parties opposed to the arrangement, claiming Hasan is a government stooge, the former judge withdrew just hours before he was due to be sworn in.
Iajuddin then proposed taking his place in a compromise that the Bangladesh Nationalist Party (BNP) - the party of Begum Khaleda Zia, the prime minister -appeared to favour. The Awami League, the main opposition group, opposed the move.
Clashes between supporters of
rival political parties and police
Iajuddin summoned the leaders of two small parties to his official residence on Sunday to discuss who should head the interim administration, a presidential spokesman said.
He said the president expected to meet BNP and Awami leaders for further talks later.
The caretaker authority is to govern Bangladesh when the outgoing government's term expires and to hand power over to a newly elected team within three months.
Fierce street battles which started on Friday continued on Sunday killing three more people to take the toll to 19, police said.
Thousands of protesters, carrying sticks and chanting slogans, gathered in central Dhaka on Sunday for an afternoon rally.
Protesters blocked roads, burned vehicles, and attacked BNP offices and the homes of ministers, police and witnesses said.
The southern port of Chittagong remained idle as the opposition enforced a strike there.