Meshaal, who has survived an Israeli assassination attempt, was speaking at a rare news conference in Damascus on Monday.
"Our people ... are united on the insistence to swap the captured soldier with prisoners in the jails of the Zionist enemy," Meshaal said.
Israel has said it will not negotiate with the governing Hamas movement for the release of the soldier, captured in a cross-border raid into Israel on June 25.
"We have told mediators and those who made political efforts [to end the issue] that we support the peaceful, calm handling of this matter but you need to understand the needs of the Palestinian people," Meshaal said.
Meshaal reprimanded other countries for focusing on the Israeli soldier, rather than on pressing Israel to halt its assault on the Gaza Strip.
The groups that seized the 19-year-old soldier have called for Israel to free more than 1,000 Palestinian prisoners.
Ehud Olmert, the Israeli prime minister, said on Monday: "Khaled Meshaal is a terrorist with blood on his hands and he is not a legitimate partner. I will not negotiate with Hamas."
Olmert also reaffirmed his commitment to redraw the Jewish settlement map in the occupied West Bank unilaterally in the absence of peace talks with the Palestinians, but acknowledged that "this will be difficult".
In the latest violence in the Gaza Strip, Israeli air strikes killed three fighters and wounded five others.
More than 50 Palestinians, including about 20 civilians, have been killed since the Israeli offensive began, Gaza residents said.
Olmert said Israel had "no particular desire to topple" the Hamas-led government despite the arrest by the Israeli military of dozens of Hamas officials and its Gaza raids.
"We haven't set a particular timetable for this operation [in Gaza]. It will continue in places, in times, in different measures that will suit the purposes that were outlined," Olmert said.
Israel tried to kill Meshaal in 1997 while he headed the Hamas bureau in the Jordanian capital, Amman.
Mossad agents disguised as Canadian tourists injected poison into Meshaal's ear.
He survived and King Hussein of Jordan, who was outraged by the incident, demanded that Israel provide the antidote.
Benjamin Netanyahu, who was the Israeli prime minister at the time, agreed and also released 19 Hamas detainees in return for the release of the Mossad agents, who had been detained by the Jordanian authorities.