The source, confirming Israeli radio stations' reports, said Ehud Olmert, the Israeli prime minister, declined to give a guarantee, arguing that "there may not be any choice" but to invade Gaza if rocket fire into Israel from the enclave persisted.
At the same time, Ehud Barak, Israel's defence minister, assured Jordan that Israel is interested in continuing an Egyptian-brokered truce, the Israeli source said.
The developments come as residents of Gaza continue to face shortage of basic food supplies due to Israel's blockade.
Most bakeries in Gaza have stopped working due to shortage of fuel and electricity and tens of thousands of poultry have been culled after running out of fodder.
The UN has criticised Israel's closure of the Gaza crossings as a "direct contravention of international human rights and humanitarian law".
An Israeli defence ministry spokesman said that continued rocket fire from Gaza towards Israel had prompted the decision to close the crossings again.
The charge by Navi Pillay, the UN high commissioner for human rights, came as Israel moved to re-seal the crossings into the Gaza Strip on Tuesday, a day after allowing lorries carrying aid into Gaza.
Pillay urged Israel to allow the flow of aid including food, medicine and fuel to resume, and to restore electricity and water services in Gaza.
She said that "1.5 million Palestinian men, women and children have been forcibly deprived of their most basic human rights for months".