Israel sees him as the brains behind the abduction and threatened to try to assassinate him.
The accusations have placed Mishaal at the centre of the vital question of who runs Hamas, which has power centres in Gaza, the West Bank and the Syrian capital - where its leadership is seen by some as the most hardline.
Mishaal has not spoken in public since Sunday's kidnapping of Corporal Gilad Shalit and is believed to have gone underground for fear of an Israeli attempt to kill him.
Meanwhile, Ismail Haniya, the Palestinian prime minister, has demanded that Israel end its armed incursion into the Gaza Strip aimed at freeing a kidnapped soldier before the situation worsens.
"The Israeli occupation must put an end to its aggression before the situation gets complicated and the crisis gets worse," Haniya said in a statement on Wednesday, adding he hoped a "positive result" could be found.
The Hamas leader also condemned Washington for "giving the green light to [Israeli] aggression in the Gaza Strip and closing its eyes to the 1.5 million Palestinian civilians who face all-out war on land, sea and air."
Interviewed by Aljazeera from Houston, USA, Amr Moussa, the Arab League secretary-general, said: "What is called Israel's right to defend itself is an absurd and anarchic logic since that means supporting the Israeli occupation of lands that belong to others."
On Wednesday, officials close to Mishaal denied he gave the green light for the capture - even as they lauded the operation.
"The resistance fighters have displayed moral and operational superiority over the Israeli army," said his aide Moussa Abu Marzouk in an interview. "They carried out an act that, I believe, the Palestinian people greatly appreciate."
Abu Marzouk says the Israeli
soldier is being treated well
The political wing of Hamas is believed to set the group's general policies and is familiar with how members of the military wing think.
For instance, Abu Marzouk insisted in the interview that Shalit is being well-treated by his abductors. "For sure, he's in hands that will protect him and treat him well. Our morals and our religion dictate that we do this to every prisoner," he said.
Asked if his statement was based on information, Abu Marzouk laughed and said: "These are facts."
Israel, however, has put the blame squarely on Meshaal.
Late on Wednesday, Hamas said the guerrilla operation in Kafr Shalom proved once more the myth of the "invincibility of the Israeli army".
In a statement, a copy of which was obtained by Aljazeera, Hamas said the capture of the Israeli soldier was a legitimate act since the operation targeted a military post and climaxed with the arrest of the Israeli soldier, which gives the resistance the right to demand the release of Palestinian prisoners in Israeli jails.
The statement considered the Israeli accusation against Hamas leaders abroad and holding them directly responsible for the operation, as an attempt to export the crisis and put further pressure on Syria.