"And we are working across many areas to ensure that we are taking appropriate and responsible set of responses to the Cheonan tragedy and provocation."
Yu said his government was satisfied with what he called "the watertight coordination at various levels" following the sinking.
Both the US and South Korea have urged the North to avoid fresh provocations and vowed to hold it accountable for the loss of the Cheonan.
Tension is high on the Korean peninsula with North Korea warning any moves to punish it over the March 26 incident would mean armed conflict.
South Korea has taken punitive measures against its northern neighbour, including trade restrictions, after accusing the North of torpedoing the Cheonan.
The sinking occurred near the two Koreas' disputed sea border, killing 46 sailors.
North Korea has vehemently rejected any role in the sinking, declaring it would cut off almost all ties with the South.
South Korea has also taken the issue to the UN Security Council, where both sides stated their case on Monday over Seoul's request for international sanctions to punish Pyongyang.
North Korea has urged the UN to impartially handle the sinking, warning that the ongoing tension over the incident could trigger a war.
In a rare news conference on Tuesday Sin Son Ho, the North Korean UN envoy, said that the North's military would respond if the Security Council questions or condemns the country over the sinking.
In a statement on Monday the council urged North Korea and South Korea to refrain from any provocative acts.
The two Koreas are still technically at war, having never signed a formal peace treaty cementing the armistice that halted the 1950-53 Korean War.