Fifty-eight crew members were rescued after the 1,200-ton Cheonan went down on Saturday near South Korea's Baengnyeong Island in the Yellow Sea.
Pyongyang 'not involved'
The disputed sea border with North Korea was the scene of deadly naval clashes in 1999 and 2002 and of a firefight last November.
However, officials in Seoul, South Korea's capital, have ruled out North Korea's involvement in the sinking.
They hope that a successful dive to the stern of the 88-metre corvette will provide clues about the fate of the missing crewmen and the cause of the blast.
The stern is 40 metres underwater.
The families of the missing have demanded swifter rescue efforts amid growing anger after divers postponed earlier attempts to reach the stern due to strong currents, poor visibility and high waves.
"Do not give up hope that there could be survivors," Lee Myung-Bak, South Korea's president, said in a statement to emergency workers on Monday.
"Look into the causes of the incident thoroughly and leave no single piece of doubt behind."
Lee has called four emergency security meetings since the sinking but has cautioned against jumping to conclusions about the cause.
Fourteen navy craft and six coastguard ships supported by aircraft were involved on Monday, plus a 3,200-ton US salvage ship with 15 divers.
US and South Korean military officials say no unusual movements have been detected by the North, which has said nothing about the incident.
North Korea refuses to accept the maritime border known as the Northern Limit Line, which was drawn up by UN forces after the 1950-53 Korean war.
It says the line should run further to the south.
In January, the North fired 370 artillery shells into the sea near the border, raising tensions between the two countries.