Rajapakse was re-elected as president following elections in January, largely on the back of popular support from the country's Sinhalese majority.
Despite his resounding victory, he lost out to Sarath Fonseka, the former army chief, in predominantly Tamil areas just months after declaring victory over the Liberation Tigers of Tamil Eelam (LTTE) separatists.
"I thank all those who voted at the presidential election," Rajapakse said.
"Even though not all voted for me, they participated in a democratic process which will lead to unity and national reconciliation."
The LTTE, which fought a 37-year war for an independent homeland in the north and east of the Indian Ocean island, controlled Jaffna until it was forced out by the military in December 1995.
However, access to the town remained limited until recently because of fighting between the separatists and government forces elsewhere in the region.
Rajapakse said he was keen to establish IT-based industries in Jaffna, 400km north of the capital, Colombo, and spur greater economic development in the area.
With the opposition deeply divided following the electoral defeat of Fonseka and then his detention, the ruling Freedom Alliance is tipped to win the April 8 polls.