In a nationally broadcast speech, Mahinda Rajapaksa, Sri Lanka's president, lauded Friday's victory.
"Our soldiers by this evening have been able to totally liberate Elephant Pass from the [rebel] clutches," he said.
In the east of the country, separatist fighters detonated a roadside bomb near the border of the Trincomalee and Anuradhapura districts, killing three air force troops and four civilians, brigadier Udaya Nanayakkara, a military spokesman, said.
The government captured the east from the rebels in 2007, but attacks in the area have increased in recent months.
If confirmed, the government's advance would deal another serious blow to the group by further isolating the separatist rebels in a section of northeastern coastal jungle around Mullaittivu, the last remaining town in the hands of the LTTE.
It is difficult to independently verify the government's claims as journalists are barred from the region.
The Tigers did not comment on the capture of the pass.
Tiger forces have been steadily withdrawing, moving artillery and heavy weapons to make a stand at Mullaittivu, military analysts say.
Human rights groups warn up to 230,000 civilians could be get caught up in the fighting there.
Tens of thousands of people have died since the LTTE began battling the government in 1983.
The LTTE says it is fighting for the rights of minority Tamils in the face of mistreatment by successive governments led by the Sinhalese majority since Sri Lanka won independence from Britain in 1948.