Tour of captured areas
Accompanied by military commanders and defence officials, Rajapakse flew by helicopter to Vakarai, part of a coastal stretch of land, with a population of about 12,500, that had been held by the Tigers for 11 years.
The village was captured by government forces in January after three months of fighting.
When asked what the government would do if the rebels refused his offer of talks, Rajapakse said his government "will have to tame the Tigers."
He said: "I don't believe in a military solution but I believe in defending my country and believe that we all are Sri Lankans."
Rajpakse spoke with about 200 people from the area and was shown rifles and anti-personnel mines said to have been left behind by fleeing rebels.
He also visited Sampur village north of Vakarai, which in September became the government's first territorial gains since a peace agreement, brokered by Norway and signed in 2002, fell apart.
The president's trip came as police arrested over 200 people on Saturday as part of a security roundup in Colombo, Sri Lanka's capital.
Earlier, 2.5kg of explosives had been found in a three-wheeler taxi parked by a cricket stadium, where troops are billeted.
"The police arrested people who could not immediately explain their presence in the area," said a police official involved in the investigation.