She also said "the international community has a responsibility and the duty to respond" to the sinking.
Al Jazeera's Tony Birtley, reporting from Seoul, said Clinton's three to four hour stopover was to show US solidarity with South Korea and to brief officials there on what China - where Clinton had just visited - was saying about the situation.
On Tuesday, Pyongyang said "from now on it will put into force the resolute measures to totally freeze the inter-Korean relations, totally abrogate the agreement on non-aggression between the North and the South and completely halt the inter-Korean co-operation," according to the official Korean Central News Agency (KCNA).
However, despite its angry rhetoric North Korean authorities allowed South Korean workers to enter the jointly-run Kaesong industrial park that is a lucrative source of income for the North.
It also did not cut military communication lines which are necessary for the Kaesong operations, Seoul's unification ministry said.
A spokesman for the ministry said the North had approved the entry of South Korean workers to the Kaesong industrial park, where companies from the South have factories employing some 40,000 low-cost North Korean workers.
The move to let in workers suggested that behind its tough stance, the isolated North was being careful not to take steps that will undermine its already tattered economy.
Seoul's financial markets, battered the previous day partly due to rising tensions on the divided peninsula, looked stable in early trading on Wednesday.
|North Korea has warned of 'all-out war' if it is punished for the sinking of the Cheonan [EPA]
Tuesday's comments from the North marked a new high in tensions on the divided peninsula after the March sinking of the South Korean warship, Cheonan, which Seoul blamed on a torpedo fired by the North.
Pyongyang has said the accusation was tantamount to a declaration of war.
Referring to the South's government as "military gangsters, seized by fever for a war", North Korea said if the South crossed into its side of the disputed sea border - the scene of deadly clashes in the past - the North would "put into force practical military measures to defend its waters".
On Monday, South Korea's president cut all trade with the North and blocked its commercial ships from sailing through the South's waters.
He also said he planned to take the Cheonan sinking to the UN Security Council and vowed that the South would forcefully defend itself should the North show aggression again.
A report by international investigators last week accused the North, already under international pressure over its nuclear programme, of torpedoing the Cheonan corvette on March 26, killing 46 sailors.
But the North accused South Korea's government of falsely blaming Pyongyang for the sinking, partly to help the ruling party in local elections due to be held next week.
On Tuesday Hillary Clinton, the US secretary of state, said that Washington and Beijing would work together to come up with an "effective, appropriate" response to the sinking.
|Seoul has pledged to defend itself against any future aggression from the North [Reuters]
She said both sides should examine the issue over time, suggesting quick UN Security Council action was unlikely.
"[China] shares with us the goal of a denuclearised Korean Peninsula and a period of careful consideration in order to determine the best way forward in dealing with North Korea," she said.
But China, the North's only major ally who in effect bankrolls its economy, has studiously tried to keep out of the fray, urging calm and refusing to voice support for the international report on the Cheonan sinking.
On Wednesday, China's foreign ministry repeated calls for calm and restraint, with Zhang Zhijun, the vice-foreign minister, saying China had no first-hand information on the sinking.
"We have always believed that dialogue is better than confrontation," Zhang said.
In Washington, a spokesman for the state department called Pyongyang's approach "odd".
"I can't imagine a step that is less in the long term interest of the North Korean people than cutting off further ties with South Korea," PJ Crowley said.
The US has said it "fully supports" South Korea's move to impose sanctions on the North, calling it "entirely appropriate".
And the White House has directed the US military to work closely with South Korea "to ensure readiness and to deter future aggression".
US and Japanese defence chiefs also discussed the issue at the Pentagon on Tuesday with Robert Gates, the US defence secretary, thanked his Japanese counterpart Toshimi Kitazawa for Japan's strong response to the Cheonan sinking.
A Japanese defence official told the Reuters news agency that the two discussed "future North Korean possible activity" during the 40-minute meeting.
The Pentagon said US, Japanese and South Korean defence chiefs would hold trilateral talks in Singapore next month on the sidelines of a security conference.
Most analysts doubt either side would deliberately risk a war, but say there is a serious risk that small skirmishes along the heavily-defended border could turn into broader conflict.
Some worry pushing Kim Jong-il, the North Korean leader, too far may leave him little choice but to fight back to try to save his family's more than 60-year hold over the destitute country as he tries to secure the leadership succession for his youngest son.