A statement from the office of Mahinda Rajapaksa, Sri Lanka's president, said he had assured Ban Ki-moon, the UN secretary-general, that the offensive "would be carried out without harassment to the civilian population".
Officials have accused the LTTE of using civilians as human shields.
Food crisis warning
The UN has, meanwhile, given warning of a food crisis in the country's north.
Emilia Casella, a spokeswoman for the World Food Programme, said in Geneva on Friday that the entire population of Vanni is facing a food crisis.
Some 250,000 people there are completely dependent on humanitarian aid, but the WFP has not been able to get a supply convoy into the conflict zone since January 16, she said.
A convoy that was supposed to enter during a four-hour "humanitarian window" on Thursday could not go because the agency did not receive the necessary clearance from government officials.
It will have to wait until next Thursday, Casella said.
"We don't have any more stocks to be distributed, and our staff are essentially hiding at the moment,'' she said.
More than 2,200 civilians are said to have fled the war zone in the last several days, official sources said on Friday.
The reported flight of civilians came after the military announced the capture of the biggest LTTE sea base.
The military released a video on Saturday showing its seizure of the base.
The fighting is concentrated around a circle of jungle in the country's northeast, where the military says it has all but surrounded the LTTE.
The US, Britain, the European Union and other major powers have urged the LTTE to surrender, and for both sides to stop firing temporarily to allow civilians out and aid in.
However, Sri Lanka's government has rejected a call by international donors for it to begin negotiating with the LTTE.
Speaking to Al Jazeera on Saturday, Ravi Sawhney, a former Indian army general and a strategic affairs analyst, said: "Basically the Sri Lankan government should be slightly more magnanimous in their victory because at the end of the day the military victory has to lead to political settlement.
"There has to be an accommodation of the Tamil Tigers aspirations."