Khaled Meshaal is exiled in the Syrian capital Damascus
The political leader of Hamas, Khaled Meshaal, says that the time has come for the West to lift its boycott on his Palestinian Islamist movement.
In a speech aired on Arab satellite TV, the exiled chief said it was "time to start talking to Hamas".
Hamas, which controls the Gaza Strip, declared a ceasefire after Israel called off its three-week offensive.
The group has claimed victory in the confrontation, saying it stopped Israel achieving its aims.
"I tell European nations... three years of trying to eliminate Hamas is enough. It is time for you to deal with Hamas, which has gained legitimacy through struggle," Mr Meshaal said in a speech from the Syrian capital, Damascus.
"Now it is time to start to talk to Hamas, which is a legitimate force."
Conditions for talks
The four main Middle East mediators - the EU, the US, the UN and Russia - have said there can be no dealing with Hamas until it recognises Israel, renounces violence and accepts interim peace deals signed by the Palestine Liberation Organisation.
Mr Meshaal said that Hamas had withstood Israel's attacks, despite its military superiority.
"The Gaza Strip has scored a victory. The enemy has failed and the resistance, together with our people and nation, has scored victory.
"This is the first war we have won, the first real and large-scale war. That is why the battle in Gaza is a real turning point in the struggle against the Zionist enemy," he said.
"But we still have two important battles ahead of us. The battle to break the siege and the battle to reopen the border crossings, particularly the Rafah crossing."
Israel has blockaded the Palestinian enclave since Hamas took control of the Gaza Strip in June 2007.
It has refused to fully open border crossings to allow desperately needed aid, goods and construction materials into Gaza.
Mr Meshaal also said the "liberation of Palestine" was no longer "just a dream".
"It is now a reality we can see, we are close to realising it, with God's grace," he said.
Israeli Defence Minister Ehud Barak also declared victory on Wednesday, as Israeli forces completed their withdrawal.
"We won in a big way," Mr Barak told Israeli Channel 2. "Hamas was dealt a blow it never imagined and will be quiet now for a long time."
Israel's military chiefs have warned that they will respond swiftly to any "provocation" from Hamas.