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By Wednesday morning, troops had captured about a third of the remaining Tiger-held area, which had been an army-declared no-fire zone until soldiers marched in and turned it into the conflict's final conventional battlefield.
"Confrontations are taking place. Whenever we come across LTTE cadres, we are fighting them. The rescue operation is continuing," military spokesman Brigadier Udaya Nanayakkara said.
The number of people who have fled this year is now around 167,000, according to the military tally.
Defence spokesman Keheliya Rambukwella told a media briefing the LTTE only had around 13 square km (5 sq mile) left, after troops seized the centre of the north-south strip of coast and divided the remaining rebel fighters into two pockets.
Later, the military said two senior rebels surrendered to troops as they fled with civilians.
Daya Master, a former schoolteacher who became the LTTE media coordinator and spokesman, turned himself in along with the translator for the late Tiger political head S.P. Thamilselvan, the military said.
For a third straight day, the military success drove the Colombo Stock Exchange higher, traders said. Provisional data showed it up 1.5 percent by late in the trading day at 0900 GMT, near a three-month high.
The massive civilian presence in the no-fire zone had been the last crucial defence for the Tigers, who refused repeated calls from the United Nations, Western governments and neighbouring India to release them.
They ignored a two-day pause by the government last week.
Sri Lanka's government subsequently rejected LTTE and international calls for a new truce, saying it cannot allow a group designated as a terrorist organisation by more than 30 countries to use the time to rearm as it has done before.
The United Nations confirmed this week's outflow.
"It is 60,000 plus and counting, and we have heard various reports of up to 110,000 coming out," said the U.N. spokesman in Colombo, Gordon Weiss. He cautioned the reports were preliminary and not confirmed.
So far, only 7,500 had reached refugee centres away from the front in Jaffna and Vavuniya towns, while the rest were in transit, he said.
Aid agencies have warned refugee camp conditions could quickly turn poor with the population doubling, but Sri Lankan President Mahinda Rajapaksa has ordered extra food and relief supplies to be sent.
On Tuesday, the International Committee of the Red Cross had said the war zone situation was "catastrophic", with several hundred killed since Monday and at least 50,000 more remaining at risk with limited food, water and medical care.
The United Nations and others have accused the LTTE of forcing people to stay in the war zone or making them fight, and the government of shelling civilian areas. Both deny the accusations.
The military operation to rescue the civilians began on Monday and gathered speed on Tuesday after the LTTE ignored a noon deadline to surrender, despite being massively outgunned by a military built up to wipe them out and end the war.
A senior LTTE official hours later said the group would never surrender nor give up its drive to create a separate state for Sri Lanka's minority Tamils, which has percolated since the early 1970s but erupted into full-blown civil war in 1983.
After the conventional end of the war, Sri Lanka will face the challenges of healing divisions between the Tamil minority and Sinhalese majority, and boosting a $40 billion economy suffering on many fronts including a weakening rupee <.LKR>.
Sri Lanka is seeking a $1.9 billion International Monetary Fund loan to ease a balance of payments crisis and boost flagging foreign exchange reserves.