Israeli prime minister Benjamin Netanyahu has warned Hamas that Israel will intensify airstrikes against the Gaza Strip if the militant group rejects the Egypt-brokered ceasefire.
"If Hamas rejects the Egyptian proposal and the rocket fire from Gaza does not cease, and that appears to be the case, we are prepared to continue and intensify our operation," he said.
The ceasefire, agreed by Israel, was set to begin on Tuesday morning but Hamas spokesman Sami Abu Zuhri claimed the group had not been consulted in the ceasefire talks.
"No one has even contacted us about this [Egypt ceasefire proposal]. We have been ignored," he said.
"We reject the ceasefire & will continue to fight. Our aim is to let people in Gaza live in dignity."
The military wing of Hamas said that the Egyptian proposal "wasn't worth the ink it was written with".
At least 35 rockets have been fired into Israel from the Gaza Strip since Israel started to adhere to Egypt's propsoal, according to the Israeli military.
Hamas police spokesman Eyad Bouzam claimed that Israel launched a strike after the start of the ceasefire but the Israeli military has denied this report.
US Secretary of State John Kerry said that he could not "condemn strongly enough" Hamas' continued rocket fire despite the call for a ceasefire from Israel and Egypt.
Attempts to agree a ceasefire come after a week-long bombing campaign by Israel on the Gaza Strip which has killed more than 192 Palestinians.
Hamas has launched hundreds of rockets into Israel but no casualties have resulted due to the presence of air raid shelters and the Iron Dome interceptor system.