(CNN) -- Sri Lanka's prime minister warned Saturday that his country "stands on the brink," as its soldiers cornered Tamil Tiger fighters in an assault that is trapping more than 50,000 civilians on a small plot of coastal land.
Sri Lanka's defense ministry says this handout photo shows troops with a captured Tamil Tiger craft Thursday.
The United Nations estimated the number of civilians, who were trapped on about 1.5 square miles (four square kilometers) of land.
Government troops seized the last remaining coastal stretch under the control of Tamil Tiger rebels, the Ministry of Defense said Saturday, marking a possible end to more than 25 years of fighting in the island nation.
The seizure marks the total capture of coastline territory previously controlled by the rebels, it said, after army divisions advanced from the north and south to link up.
An army source told CNN that about two square kilometers in the region remain to be captured, and that military officials expect that to happen in a couple of days.
The rebels -- formally known as the Liberation Tigers of Tamil Eelam (LTTE) -- have fought for an independent state for minority Tamils in Sri Lanka since 1983. As many as 70,000 people have been killed since the civil war began.
"Sri Lanka stands on the brink," Prime Minister Rathnasiri Wickremanayake said in a written statement. Watch aid agencies fear for Sri Lanka »
"We have called repeatedly for the violence to cease. The humanitarian agencies must be granted access to civilians caught in the crossfire of a dreadful conflict. Watch iReporter Thileepan's footage of the "safe zone" »
"We are backing U.N. efforts to secure an orderly end to the conflict. The LTTE must lay down its arms and allow civilians to leave. Sri Lanka must understand that there will be consequences for its actions."
No formal declaration of victory is expected at least until Sri Lankan President Mahinda Rajapaksa returns to the country from Amman, Jordan, where he is attending the World Economic Forum.
In an address to the summit in Amman on Saturday, Rajapaksa said the Sri Lankan armed forces had defeated the rebels.
"I will be going back to my country Sri Lanka that has been totally freed from the barbaric acts of terrorism of the LTTE. This freedom comes after 30 long years."
"Our economic prosperity must essentially rest upon global peace and stability. Terrorism has for decades denied us this right. All eleven countries gathered here today have suffered the effects of terrorism, some more than others.
"Terrorism has raised its ugly head in different forms from time to time and destroyed all development initiatives in most of our countries" he said.
On Friday, the Navy arrested the wife of Soosai, a leader of Sea Tigers -- the ocean-going arm of the rebel group. His daughter and son-in-law were also arrested.
Navy officials, quoting those who were arrested, said Tigers leader Velupillai Prabhakaran is believed to be inside the area of the latest fighting. Other sources have said he has escaped.
CNN's Iqbal Athas contributed to this report.