"I believe that all political forces should be united to find solutions to the serious problems of our nation," she said in a speech to mark the country's 56th independence anniversary on Wednesday.
Kumaratunga took over the defence, interior and media ministries from Prime Minister Ranil Wickremesinghe's government in November, saying the premier had compromised security in his peace attempt with the Liberation Tigers of Tamil Eelam (LTTE).
Her move stalled efforts to resume peace talks with the rebels, leaving the president - whose People's Alliance party is in the opposition - and the prime minister bickering over how the peace process should proceed.
"I do not think my actions have in any manner weakened the current peace process," said Kumaratunga.
As the impasse between Kumaratunga and Wickremesinghe drags on, speculation has increased she might dissolve parliament and call fresh elections, but the president was silent on the issue.
Elections would further delay peace talks with the Tigers, which Wickremesinghe has said he wants to restart.
Both sides want to complete the two-year old ceasefire with a political agreement to end 20 years of civil war.
The president has been mum on
speculation of early polls
But Wickremesinghe refuses to handle the peace process while Kumaratunga controls security.
"We must appreciate the commitment shown by the LTTE and all political parties to peace through the continuation of the ceasefire," said Kumaratunga, flanked by generals of the Sri Lankan army, of which she is commander-in-chief.
After her speech, Russian-made T-55 tanks, multi-barrel rocket launchers and howitzers rolled through Colombo's Independence Square in the first show of heavy weaponry since the celebrations of 50 years of independence in 1998.
A military spokesman said the display was not meant to intimidate the Tamil Tigers.
"When the war was on, we had no opportunity to show these arms, because they were involved in battle," he said.
Protests in the north
In the north of the island, monitors overseeing the ceasefire said dozens of farmers thought to be backed by the Tigers blocked the checkpoint dividing government and rebel territory, leaving about 200 people stranded.
"They are hoisting black flags, but the situation is calm. There is no tension there," said Agnes Bragadottir, spokeswoman for the Sri Lanka Monitoring Mission.
The Tigers complain that, despite the ceasefire, not enough has been done to rebuild the war-shattered north.
"4 February is not an Independence Day for the Tamil people. It is a day of mourning," the rebel-backed Vavuniya North Consortium of People's Organisations said in a statement.