He said ministers of state would be appointed next week.
Gotabhaya Rajapaksa as the President cannot hold ministries although he is the head of the Cabinet.
The Tamil minority members came from the Tamil dominated north and from the central tea plantations areas of Tamils of Indian origin.
Mahinda Rajapaksa, who is appointed on the post of the Prime Minister in the new Cabinet, was also named as the Minister of Defence and Finance while the eldest of the brothers Chamal Rajapaksa was named the Minister of Trade and Food Security.
Dinesh Gunawardena, 70, a veteran Marxist politician has been named as the Minister of Foreign Affairs.
The Cabinet appointment is seen as interim until the President dissolves the current parliament and go for a fresh parliamentary election.
The next parliamentary poll is scheduled only after August 2020. Constitutionally, a sitting prime minister cannot be removed unless he resigns. But following Gotabaya Rajapaksa's win, the need for a fresh parliamentary poll to allow the new president to form his own government has gained ground.
Gotabaya Rajapaksa could dissolve the current Parliament to call for early elections after February 2020.
Speaker Karu Jayasuriya on Tuesday said that the country faces the possibility of a snap parliamentary poll.
Prime Minister Ranil Wickremesinghe is also under pressure to quit.
"As a party which honours democracy, we will discuss with parliamentary group, the Speaker and party leaders about parliamentary elections," a statement from Wickremesinghe's office said on Monday.
Gotabaya Rajapaksa was on Monday sworn in as Sri Lanka's seventh President. He defeated Sajith Premadasa, 52, by more than 13 lakh votes.
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