The United States and the European Union have urged the president to immediately summon parliament and let deputies decide who is to lead the country.
Karu Paranavithana, a lawmaker from Wickremesinghe's United National Front, welcomed the announcement, calling it "a great victory" for the people.
Sirisena was supported by Wickremesinghe three years ago but the two men have gradually drifted apart, leading to Wickremesinghe's shock sacking last month. Sirisena suspended parliament until Nov 16 and has made no public statement on his plans.
Severely criticizing the policies of the Wickremesinghe government, the President said the ones who took decisions regarding the country in the recent past were not the President or the Prime Minister, but a "gang of butterflies" who were around Ranil Wickremesinghe.
So far Rajapaksa has 100 MPs on his side while sacked prime minister Ranil Wickremesinghe has 103 MPs in the 225-member assembly.
As a result new Prime Minister Mahinda Rajapaksa will not be given the Prime Minister seat in Parliament as the current Government members will need to sit in the opposition seats.
"I have to agree with the majority of parliament who believe that the president's actions are undemocratic, unconstitutional and against all norms of parliamentary procedure", added Jayasuriya, who is originally from Wickremesinghe's United National Party but holds a neutral position in parliament.
Rajapakse has also already assumed duties as Finance Minister, announcing last week a slew of tax concessions and price cuts in a move seen as a sop to voters.More news: Alec Baldwin Arrested For Punching Man In The Face Over Parking Spot
The sudden development came amid growing tensions between Sirisena and Wickremesinghe on several policy matters and the President has been critical of the Prime Minister and his policies, especially on economy and security.
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While stressing that they won't allow anyone to break the unity between the President and the Prime Minister by spreading rumours, the Premier also requested all the minority political parties to join with them on behalf of their people in each and every part of the country to develop the country.
The rally held to show support to newly appointed Prime Minister and the government has been named "Ratama Rakina Jana Mahimaya".
However, on Thursday evening, General Secretary of the United People's Freedom Alliance (UPFA) Susil Premajayantha told journalists that no such announcement had been made by the president and parliament would convene as announced on November 16.
Rajapakse-led Sri Lanka Podujana Peramuna said a new caretaker cabinet will be sworn in on Monday.
Among the massive crowds were farmers, state and private sector employees, trade union members, professionals and ordinary public.