Mishaal was speaking at a ceremony on Thursday to mark the start of the final 10 days of Ramadan.
"Hamas will not surrender to those wanting to mount a coup against it, will not recognise Israel and will not abandon armed resistance," he said.
Since being elected in to power earlier this year, the Hamas-led government has been under intense financial pressure due to sanctions imposed by the US, Israel's chief ally, and the EU and by Israel's policy of withholding taxes due to the government.
The funds are being withheld on the grounds that Hamas does not recognise Israel and has refused to give up the armed struggle against the Israeli occupation and has not accepted previous peace accords.
Hamas has, however, offered a truce in return for a Palestinian state along the 1967 border.
Mishaal, who lives in exile in Syria, said Hamas's position would eventually pay off.
Mishaal said: "Let's ... force Israel to compromise. Let us keep some cards in our possession. We have seen the fate of those who accepted recognition as a precondition for negotiations. They have gained nothing.
"Does non-recognition prevent political dialogue? China doesn't recognise Taiwan. States sometimes don't recognise each other, yet still have ties."
He said Hamas could live peacefully along side Israel if Israel gave back Palestinian land occupied since 1967, including East Jerusalem, and gave refugees their rights.
Aides to Mahmoud Abbas, the Palestinian president and the leader of Fatah, have said he may appoint an emergency government or call early elections after the latest efforts to form a unity government with Hamas failed.
Mishaal said a Palestinian unity government with Abbas's Fatah movement was still possible despite the collapse of mediations and an upsurge in violence between the two groups.
"A joint Palestinian government could be formed if we listen to our prisoners, the cries of our wounded and the souls of our martyrs," he said.