Fawzi Barhum, a Gaza-based spokesman for Hamas, told news agency AFP that "there was no possibility of renewing the truce".
While neither side has said it will go on the offensive, Barhum underlined: "We at Hamas have the right to respond to any Zionist aggression against the Palestinian people. It is a national duty."
"We can expect to see a continuation of low-level hostilities that we saw up until June, when the ceasefire was announced"
Jacky Rowland, Al Jazeera's correspondent in Jerusalem
Israel has not yet issued an official response to the Hamas announcement, but Ehud Barak, the Israeli defence minister, had indicated earlier that Israel would respond if attacked.
"When the situation requires us to, we will act... we are not afraid of launching a large-scale military operation in Gaza, but there is no need to rush into it," he said.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said that Palestinians had been hoping the ceasefire would improve everyday life - bringing fighting to an end and increasing access to food and other goods via re-opened crossings.
However, Hamas and other Palestinian groups said Israeli infractions of the truce - both security violations in Gazan waters and territory and its crippling blockade of the Strip - rendered the ceasefire meaningless.
"That [improvement] hasn't happened and therefore the Palestinian factions have concluded that the truce hasn't brought about any tangible difference," he said.
Mohyeldin also said that ordinary Gazans were aware the failure to renew the ceasefire could bring about an escalation in fighting "and a resumption of Israeli targeted killings of various military and political leaders" in Gaza.
"This has huge consequences for Gaza's population, civilians often bear the brunt of military activity coupled with the siege," he said.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "Hamas is blaming the end of the ceasefire on Israel, but Israel would probably blame it on Hamas. First of all, because it is Hamas who says it is over," she said.
However, Rowland noted that Israel had been keen to extend the Egyptian-brokered truce - particularly as the country is expected to hold a general election in February next year.
"In the short to long term, we can expect to see a continuation of low-level hostilities that we saw up until June, when the ceasefire was announced," she said.
"We can expect to see rocket fire ... and Israeli attacks from the air, trying to take out those rocket launchers."
Both sides blame each other for violating the ceasefire, with Israel saying it will re-open crossings and end military operations when Gazan fighters stop launching rocket attacks on southern Israel.
Hamas stopped short of threatening an escalation in military action and both sides appear wary of provoking a full-scale confrontation, possibly even an invasion, that could cause heavy casualties on both sides.