The army has been advancing north after taking Kilinochchi
The Sri Lankan army has captured Elephant Pass, the strategic causeway linking the Jaffna peninsula with the mainland, the president has said.
Mahinda Rajapaksa said Tamil Tiger rebels had been completely dislodged. The Tigers have made no comment yet.
Troops took Kilinochchi, the HQ of the rebels, last week and began a pincer movement on Elephant Pass.
The Tigers have been fighting for a separate homeland for 25 years and have held the pass since 2000.
De facto state
President Rajapaksa said in a televised address: "Our forces have recorded another historic victory. That is the complete dislodging of the Tigers from Elephant Pass and the security forces establishing their authority there."
On Thursday, troops coming south from Muhamalai took over the rebel base at Pallai and then advanced 5km (3 miles) further south to capture Sorampattu, the military said.
Other troops had reached the southern outskirts of the pass after taking Kilinochchi and Paranthan.
Analysts say the government is now in control of the A9 highway and can supply troops and the residents of Jaffna by land. The rebels had held a 100km (60 mile) stretch since 2000, forcing the government to use expensive sea and air routes.
The news of the capture sparked celebration among many residents of the capital Colombo.
The Tigers, who are fighting for a separate homeland in the north and east, had established a de facto state squeezed between government-controlled Jaffna in the north and the rest of the country.
But the latest military offensive has forced the rebels to give up much of their territory.
Sri Lanka's government has vowed to destroy the Tigers. At least 70,000 people have been killed in the 25-year rebel insurgency.
The focus now falls on the sole remaining major Tiger base, at Mullaitivu in the east.
The ministry of defence website says the army is making steady ground along the A35 road from Paranthan to Mullaitivu.
Separately, the military said a roadside bomb set off in the east by rebels had killed seven people.
The blast took place at Morawewa, outside the city of Trincomalee, on Friday morning as a convoy escorted by troops passed by, a statement on the defence ministry website said.
The dead included three air force personnel. Six people were injured in the attack.
The pro-Tamil Tiger website TamilNet meanwhile reported that Sri Lankan army artillery fire had killed at least four people at Tharmapuram, which it says is a centre of displaced civilians.