In the absence of a deal, Israel has ordered its ground forces to focus on locating and destroying a warren of tunnels.
Israeli Prime Minister Benjamin Netanyahu, facing international alarm over a rising civilian death toll in Gaza, said on Thursday he would not accept any ceasefire that stopped Israel completing the destruction of tunnels in and out of Gaza.
"We are determined to complete this mission, with or without a ceasefire," Netanyahu said in public remarks at the start of a meeting of his full cabinet in Tel Aviv.
"I wont agree to any proposal that will not enable the Israeli military to finish this important task, for the sake of Israel's security."
Leaving open the option of widening a ground campaign in the Hamas governed Gaza Strip, the Israeli military said it had called up an additional 16,000 reservists. A military source said they would relieve a similar number of reserve soldiers being stood down.
Netanyahu's security cabinet on Wednesday approved continuing operations launched on July 8, which has claimed at least 1,372 Palestinian lives, most of them civilians, while nearly 7,000 have been wounded.
Washington has also, however, allowed Israel to tap a local U.S. arms stockpile in the past few weeks to replenish its grenades and mortar rounds, a U.S. defence official said on Thursday.
Rolling Israeli ground assaults on residential areas, preceded by mass warnings to evacuate, have displaced more than 200,000 of Gaza's 1.8 million Palestinians. The tiny territory's infrastructure is in ruins, with power and water outages.
"Progress has been satisfactory, and we are completing our treatment of the terror tunnels," Defence Minister Moshe Yaalon said on Thursday. "During the fighting, soldiers are finding new tunnel shafts, and they are also being neutralised."
Major General Sami Turgeman, chief of Israeli forces in Gaza, said on Wednesday they were "but a few days away from destroying all the attack tunnels". The army said 32 of the secret passages had been found so far and half of them blown up.
Both sides have voiced openness to a truce, but their terms diverge dramatically. Israel wants Gaza stripped of infiltration tunnels and rocket stocks. Hamas rules that out, and seeks an end to a crippling Gaza blockade enforced by Israel and Egypt.
Diplomacy to end the Gaza conflict is further complicated by the fact Israel and the United States shun Hamas as a terrorist group, while the go-betweens - Egypt, Qatar and Turkey - disagree on Gaza policy.
Amos Gilad, a senior Israeli defence official involved in talks with Cairo, said Egypt wanted the fighting to stop before any wider negotiations on a long-term arrangement to prevent future flare-ups.
"The Egyptians don't want to discuss anything with anyone while violence and terror continue," he told Israel Radio.