A delegation from former president Maithripala Sirisena's Sri Lanka Freedom Party met him in the morning to press for their demand on the formation of the interim government.
Rajapaksa's move signalled that he would contest the snap polls, to be held on January 5, under his own party banner and not that of Sirisena's SLFP.
After nearly two days of political deadlock, the stakeholders are engaged in prolonged talks to try and appoint a successor to Mahinda Rajapaksa.
The dissidents, led by former president Sirisena's Sri Lanka Freedom Party, would leave the ruling Sri Lanka Podujana Peramuna coalition with its 14 Members of Parliament, party sources said after their meeting with the President on Monday.
Sri Lanka's new Finance Minister Ali Sabry on Tuesday resigned, a day after President Gotabaya Rajapaksa appointed him after sacking his brother Basil Rajapaksa amidst the island nation's worst economic crisis.
Sri Lankans were on the edge on Tuesday as they waited whether embattled Gotabaya Rajapaksa will honour his offer to resign as president, amid signs that key members of the erstwhile powerful ruling family were attempting to flee in the face of massive public anger against them for mishandling the economy that has bankrupt the country.
The swearing in ceremony was held inside the premises of the Presidential Secretariat at 9:30 am. President Sirisena administered the oath of office to 66-year-old Wickremesinghe, who has already served three times as the prime minister.