Sri Lankan troops marched into the Tamil Tigers' de facto capital of Kilinochchi for the first time in a decade.
An official said the town is about to fall into government hands, in what would be a major blow for the rebels.
The Sri Lankan military has had a series of recent battlefield victories against the Tigers and vowed to defeat the group this year to end their more than 25-year-old separatist war.
"(The) fall of Kilinochchi soon will be a reality," said defence ministry spokesman and government minister Keheliya Rambukwella.
Sources from President Mahinda Rajapaksa's office said that troops had entered Kilinochchi from two locations and that fighting with rebels was going on.
Military sources said an announcement was expected soon from Rajapaksa.
State media said the military had surrounded Kilinochchi and that many rebels had fled.
The Liberation Tigers of Tamil Eelam (LTTE) had no immediate comment.
Defence analysts said the fall of Kilinochchi would be a bitter blow for the LTTE.
"This is a major defeat for the LTTE. The fall of Kilinochchi means the LTTE will have their only territory in Mullaitivu," said Iqbal Athas, a defence analyst with Jane's Defence, referring to a rebel stronghold in the northeast.