Rajapakse, known for his hawkish views on the separatists, promised on Saturday to respect a 2002 ceasefire, but warned he wanted a Norway-brokered truce reviewed.
"I want to state the dedication of my government to upholding the ceasefire [but] I am also ready to review the ceasefire agreement," the socialist leader, who was previously prime minister, said in an address to the nation after taking the oath of office.
There was no immediate reaction from the Liberation Tigers of Tamil Eelam (LTTE) who were accused by local and foreign poll monitors of forcing a boycott of the vote in areas held by them.
Analysts said the Tamil votes could have spelt victory for Rajapakse's rival in the closely fought presidential race.
The 40-minute inauguration was marked by Kandyan dancing, which is traditionally performed at religious processions and weddings, and ended with a 21-gun military salute.
Rajapakse, who celebrated his 60th birthday on Friday, won 50.3% of the popular vote in Thursday's presidential ballot, beating market-friendly Ranil Wickremesinghe, who polled 48.4%.
The new president will hold office for six years.
"From this moment I will work towards my goal of making a new Sri Lanka," Rajapakse said in Sinhalese. "I will try to achieve honourable peace for all. We will discuss peace talks with the LTTE and all political parties.
"When the LTTE says they are ready to return to peace negotiations we will start talks with them immediately. We will give priority to those talks."
Peace talks between Colombo and the Tigers have been deadlocked since April 2003.
Rajapakse (C) said the Norwegian
led peace talks had shortcomings
During campaigning, Rajapakse had said he wanted to revisit the entire Norwegian-led peace process, leading the Tigers to brand the movie star-turned-prime minister as the "war candidate".
"It is an acknowledged fact that the ongoing peace process has certain shortcomings," Rajapakse told state television on the eve of the vote.
"If that is the case, the peace process has to be revised. Each and every step that was taken in the direction of peace has failed so far."
News of his election victory was greeted with caution by those driving the peace process, with two former Norwegian peacebrokers saying his taking over the reins of government could lead to deeper divisions and a rocky period.
"The situation could be very difficult," Development Aid Minister Erik Solheim told Norwegian news agency NTB.
Another ex-mediator, former state secretary Vidar Helgesen, said Rajapaske's election could cement the divisions in the country where more than 60,000 people were killed in three decades of fighting between 1972 and 2002.
The new president said in his address he would start diplomatic consultations "with all friendly nations who have helped in the peace process".
He also said he would create a new body to help with tsunami reconstruction, but did not elaborate. At least 31,000 people were killed in Sri Lanka by the 26 December tsunami and around a million displaced.
With him taking the office of president, the cabinet stands dissolved and he said new ministers would be named shortly. He also said he was ditching the national budget for 2006 presented by his predecessor.
Wickremesinghe received only
48.4% of the country's votes
"I have decided to bring before parliament new budget proposals based on the Mahinda Chintanaya (my philosophy) we presented to the people. I believe it is necessary to begin my term of office with the people's confidence in me intact," he said.
In his pre-election promises, he had offered a plethora of subsidies, including free food for children, cheap fertiliser and duty-free cars for public servants.
The United States, meanwhile, condemned what it called interference by the separatists in the island's democratic process, saying the Tigers had intimidated voters in the presidential elections.
Poll monitors said many minority Tamil voters were forced out of Thursday's elections by rebels, who used intimidation and violence to prevent them from voting.