The concern is that any such strike could escalate into a bigger conflict on the Korean Peninsula, which is already tense because of North Korea's nuclear program and recent naval clashes between the two Koreas.
The 1,200-ton ship Cheonan went under March 26 in the Yellow Sea after an explosion and 46 of the 104 sailors aboard either died or are reported missing.
An international team of experts probing the incident announced its finding Thursday, saying the ship was torpedoed by a North Korean submarine. The North denied it.
South Korean President Lee Myung-bak summoned an emergency meeting of his top security advisers to consider counter-measures.
"In the short-term, I do not expect any military retaliation, or escalation that would result in a large-scale military conflict or war," Daniel Pinkston, analyst at Seoul's International Crisis Group, told Yonhap news agency.
However, he warned of the danger of inadvertent escalation or miscalculation in the long term.
Lee was quoted as telling Australian Prime Minister Kevin Rudd by telephone his government will take countermeasures and make North Korea admit its wrongdoing.
CNN reported that under a mutual defense treaty, the United States would need to defend South Korea against any aggression.
However a U.S. military official said: "I don't think it will come to that. They know they need to have a response, but there is too much at stake for South Korea to have a confrontation on the Korean peninsula. North Korea has nothing to lose, but South Korea is a serious country with a huge economy."
John Delury, a Korea expert at the Asia Society, told CNN other military options for South Korea could include increasing its naval presence along the maritime divide with North Korea, but noted that might trigger a conflict.
Nicholas Szechenyi at Washington's Center for Strategic and International Studies told CNN, "You have to be careful about military retaliation because North Korea has thousands of artillery pieces pointed towards the south and could bombard Seoul very quickly."
Other measures could include seeking further action by the U.N. Security Council. But Szechenyi said, "The problem is that China is a permanent member of the council and tends to take a very soft position on North Korea, so it is an open question whether the resolution will pass or not."
He suggested South Korea might ask the United States to put North Korea back on the list of state sponsors of terror. The North was removed from the list in 2008 as part of a process to convince North Korea to give up its nuclear program in exchange for massive economic aid.