Former Palestinian foreign minister Mahmoud Zahar announced the Hamas proposal at a meeting with Egyptian intelligence head Omar Suleiman in Cairo.
Mr Zahar said the truce must be mutual and include the lifting of an Israeli blockade of Gaza.
He gave the proposals to Egyptian negotiators, who were expected to pass them on to Israel.
Israeli officials said they were skeptical about the chances of a truce.
Hamas described the proposed truce as a "period of quiet".
Israel said it was ready for "quiet" on its border with Gaza, but has demanded a stop to rocket attacks against Israelis and weapon smuggling into the coastal strip.
On Thursday, the UN said that it had halted food deliveries in Gaza because it had run out of fuel.
More than 80 percent of Gaza's population rely on aid, with UN food hand-outs going to about 1.1 million people - many them children.
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