Maithripala Sirisena has already received the backing of more than 40 lawmakers who were previously loyal to Mahinda Rajapakse, whom he unseated in Thursday's presidential election, spokesman Rajitha Senaratne said.
"We now have more than we need in parliament," Senaratne told AFP.
"We can have our legislative programme approved without any difficulty whatsoever."
Sirisena previously had the backing of 89 lawmakers and needed another 24 to secure a simple majority in the 225-member house.
The new leader, who is himself a defector from Rajapakse's party, has already pledged to reverse many of the constitutional changes brought in by his predecessor which gave huge powers to the president.
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Even Rajapakse's Sri Lankan Freedom Party has said it will support Sirisena's constitutional reforms, making their enactment a formality.
Sirisena quit Rajapakse's cabinet in November to emerge as an opposition unity candidate in the January 8 polls, triggering the biggest defection of lawmakers from a government since independence from Britain in 1948.
In his speech in Kandy, Sirisena is expected to spell out his reform plan in detail and call for a normalising of relations with the European Union as well as other Western nations and neighbouring India.