"There must be a commitment by Israel, to end all its aggression against our people, assassinations, killings and raids, and lift the (Gaza) siege and reopen the crossings," Hamas' Gaza leader Ismail Haniyeh said in a speech.
A ceasefire deal, he said, should be "reciprocal, comprehensive and simultaneous" and apply both to the Hamas-controlled Gaza Strip and the West Bank.
"We will not abandon you, our people in the West Bank," Haniyeh said. "Aggression against you is aggression against us."
There was no immediate Israeli comment on Haniyeh's remarks.
He delivered the address several hours after Israeli troops killed an Islamic Jihad militant in the occupied West Bank, an incident which a Hamas official said showed that Israel "was not interested in calm".
A truce could be key to the success of US-brokered peace talks between Israel and Palestinian President Mahmoud Abbas, whose Fatah faction lost control of the Gaza Strip to Hamas Islamist fighters last June.
The number of cross-border rocket attacks from the Gaza Strip has decreased sharply since Israel ended an offensive in the territory nine days ago after killing 120 Palestinians, about half of whom have been identified as civilians.
Egypt has stepped up truce efforts, amid Israeli leaders' insistence they are not negotiating with Hamas, which has spurned Western demands to recognize Israel and renounce violence.
A deal to reopen crossings could also include a prisoner exchange involving Palestinians held in Israeli jails and an Israeli soldier seized by Gaza militants in 2006.