His comments follow a meeting on Thursday with ICC chief prosecutor Fatou Bensouda to discuss the steps Thailand would be required to take if it is to accept ICC jurisdiction.
United Front for Democracy against Dictatorship lawyer Robert Amsterdam petitioned the ICC in January 2011 to launch a preliminary investigation into the alleged killings of civilians by security forces during the 2010 protests under the basis of "crimes against humanity".
The foreign minister insisted that by extending the jurisdiction to the ICC, the government would not be inviting the international tribunal to interfere in the country's internal affairs.
Thailand has not ratified the treaty that founded the ICC. The court's jurisdiction, however, can be established if the country makes a declaration accepting the court's power on an ad hoc basis.
Mr Surapong shrugged off criticism that such an agreement would become politically explosive and that he was under pressure from the red shirts to proceed with the issue.
"It is to deliver justice to those who died," he said.
"Personally I think the government should accept the ICC's ad hoc jurisdiction on the clashes," he said.
Pheu Thai list-MP Jarupan Kuldilok, a member of the House committee on foreign affairs, supported ICC jurisdiction. Ms Jarupan said Mr Surapong could sign a declaration accepting ICC jurisdiction without seeking parliamentary approval necessary for legally binding matters involving national sovereignty. The declaration is not a law, she said.
Deputy Commerce Minister Nattawut Saikuar, also a red-shirt leader, agreed with the move too.
"If the ICC is a channel the government can use to administer justice, the government shouldn't block it," he said.
Spokesman for the opposition Democrat Party Chavanond Intarakomalyasut, however, said he believed the military operation during the 2010 protests did not fall under the ICC's jurisdiction, but the Thaksin Shinawatra administration's war on drugs did.
"The operation is an internal affair and it has been investigated under Thai law. The ICC can't step in," he said.
Still, he urged the government to ratify the ICC treaty and allow it to look into all cases of "crimes against humanity".
"If we ratify the treaty, I think Thaksin will appear before the ICC before former prime minister Abhisit [Vejjajiva] and former deputy prime minister Suthep [Thaugsuban]," he said.
Democrat list-MP Kasit Piromya also filed a petition with the ICC seeking a probe into the deaths of those killed during the Thaksin administration's war on drugs. The former foreign minister in the Abhisit administration said it is ridiculous for the Yingluck government to cherry-pick issues for ICC scrutiny.