Clinton told North Korea to stop its "provocation and policy of threats" and said the world must respond to the torpedo attack on the warship.
She is meeting President Lee Myung-Bak and Foreign Minister Yu Myung-Hwan before returning home.
Meanwhile, South Korea’s military is trying to track four North Korean submarines, which have disappeared from the radar after leaving their base earlier this week:
Deputy Defence Minister Chang Kwang-Il said the submarines appeared to be on a routine military exercise but the authorities are closely monitoring the situation.
Four 300-tonne submarines disappeared from the screens after leaving Chaho naval base in the North’s north-eastern province of Hamkyong.
The United States announced on Tuesday a plan to carry out an anti-submarine exercise in the Yellow Sea with the South Korean navy and the US and Japanese defence ministers, Robert Gates and Toshimi Kitazawa, vowed unified support for South Korea in Washington on Tuesday.
Last week, an international investigation accused the North of sinking one of South Korea’s warships in a submarine torpedo attack in March.
The North denies any involvement with the sinking in which 46 sailors died. It said Tuesday it is breaking all links with the south in protest at the accusations for as long as South Korea’s President Lee Myung-Bak is in power. It has called for its own investigation.
China did not join in international outcry after a multi-national report found the North was the most likely culprit in the Chenoan sinking. The North says the evidence was faked by the South. China has the power to veto UN sanctions against Pyongyang.
It is North Korea’s main source of food, fuel and finance. It has called for restraint on both sides and has promised to objectively assess the findings of the international investigation. The Chinese Prime Minister Wen Jiabao is going to Seoul on Friday. It has not said whether it will complete its assessment by then.
South Korea vowed Wednesday to punish North Korea for sinking its warship, the Chenoan, on 26 March.
North Korea's military accused the South Korean navy of trespassing in its waters on Tuesday, and threatened military action in response.
The North says it will block access to a jointly-run industrial estate if the South restarts its cross-border propaganda broadcasts. It threatened to open fire to anyone making anti-North statements into a loudspeaker.
The South has halted most of its trade with the North and is pushing for international sanctions via the United Nations.
“There is no need to show any mercy or patience for such confrontation maniacs, sychophants and traitors and wicked warmongers as the Lee Myung-Bak group,” said a government statement.