State media in the North reported on Sunday that more than 100,000 people attended an anti-South rally in Pyongyang. Demonstrators denounced Lee Myung-bak, the South Korean president, as a traitor, and a government official warned citizens to prepare for an attack by the US and South Korea.
As a permanant member of the UN security council, China has the power to veto any resolution or statement against North Korea.
Pressure on China
Wen offered his condolences to the dead sailors, but did not mention North Korea during his statement.
Lee, the South Korean leader, indicated that he would continue to pressure China to support a security council resolution against the North.
"China and Japan have very important roles to play in the international community and I fully expect them to have wisdom on this issue," he said, in reference to the sinking of the Cheonan.
"I believe we need to take concrete measures on this matter in order to accomplish peace and prosperity on the Korean peninsula."
Yukio Hatoyama, the Japanese prime minister, echoed South Korea's calls for the North to be held to account, and said that China should support action against the secretive regime in Pyongyang.
But Wen maintained China's non-aligned position, although he did say that Beijing would protect no-one found to be definitively responsible for the attack.
Al Jazeera's Tony Birtley, reporting from Seoul, said that Wen's position was no surprise. "He spoke the words that people expected but didn't want to hear. There was some flawed hope that maybe Premier Wen would come out and stand behind the international community to have some sort of action that would go through the security council and probably help to dissipate this crisis, but he didn't."
Analysts said that China was attempting to ride out the storm on the Korean peninsula and its position reflected a confidence that the situation would improve.
"With regard to the Cheonan, China seems confident that tensions will eventually diminish," Stephanie Kleine-Ahlbrandt, the North East Asia project director for the International Crisis Group, a non-government advisory organisation, said.
Few predict that the crisis will end in war, but North Korea has raised the possibility of conflict if it is slapped with sanctions over the incident, dismissing the South Korean government as "military gangsters, seized by fever for a war".
The spat has already seen the North cut all ties with the South, scrap pacts aimed at averting accidental flare-ups along their disputed sea border and vow to attack any intruding ships.