The Israeli cabinet approved a 24-hour extension of its cease-fire Saturday but said it would respond to any future rocket fire from Gaza after Hamas rejected an earlier proposed four-hour extension and fired rockets into Israel.
The announcement came after Hamas confirmed that it fired five rockets at Israel late Saturday after rejecting an earlier offer from Israel to extend a 12-hour humanitarian cease-fire by four hours, casting new doubt on international efforts to broker an end to 19 days of fighting.
The terror group said two of the rockets were aimed at Tel Aviv. Police in Israel's second-largest city dispersed a peace rally attended by several thousand people because of the threat, a spokesman said.
Hamas spokesman Sami Abu Zuhri said the group rejected Israel's proposal to extend an original 12-hour lull by four hours, until midnight (2100 GMT) Saturday.
Meanwhile, the Israeli military warned residents of areas where there had been heavy fighting against returning there.
Israel has set its own terms for the lull, saying it would continue demolishing Hamas military tunnels under the Gaza-Israel border.
The initial lull agreed to by Israel and Hamas had begun at 8 a.m. (0500 GMT) Saturday.
In Paris, U.S. Secretary of State John Kerry and European foreign minister had been discussing how to build on the initial 12-hour lull Saturday and transform it into a sustainable truce.
The meeting included representatives from Turkey, Qatar, Germany, Italy, Britain and European Union foreign policy chief Catherine Ashton. No representatives from Israel, Hamas or the Palestinian Authority were present.
Separately, the top office of the top United Nations envoy in the region, Robert Serry, said he had been urging Israel and Hamas to extend the truce by 24 hours.
Israel wants more time to destroy tunnels and rocket launching sites in Gaza, while the territory's Hamas rulers want international guarantees that an Israeli and Egyptian border blockade will be lifted.
The Israeli government has also begun suggesting that Gaza be demilitarized as a condition for a permanent cease-fire so that Hamas cannot rearm itself ahead of yet another round of fighting. The current war is the third in Gaza in just over five years.
"We are looking for a long cease-fire, not only 12 hours," said Gaza resident Mohammad Abu Shaaban before the Israeli announcement. "We hope the cease-fire will continue and not to return back to the killing and destruction."
Meanwhile, Gaza residents used the pause in hostilities to stock up on supplies and survey the devastation from nearly three weeks of fighting, as they braced for a resumption of Israel's war on Hamas.
In the northern town of Beit Hanoun, the main road was impassable in parts due to the debris from the damaged homes. The town's hospital had been hit by a tank shell, power lines were dangling and dead donkeys were strewn on the street. A man was hitting his head and wailing "my house, my house."
Israel and Hamas began the 12-hour pause in hostilities at 8 a.m. (1:00 a.m. EST, 0500 GMT) Saturday after intensive regional shuttle diplomacy by Kerry failed to produce a longer truce aimed at ending nearly three weeks of fighting.
The temporary lull appeared unlikely to change the course of the current hostilities amid ominous signs that the war was spilling over into the West Bank and a warning by Israel's defense minister that it might soon expand its Gaza ground operation "significantly."
The Israeli military said its troops "shall respond if terrorists choose to exploit" the lull to attack Israeli soldiers or civilians. The military also said "operational activities to locate and neutralize tunnels in the Gaza Strip will continue."
Previous humanitarian cease-fires have been cut short by a resumption of fighting, but the pause on Saturday appeared to be holding, as residents returned to the streets and packed into banks and grocery stores.
Israel launched a major aerial offensive in Gaza on July 8 and later sent ground troops into the Hamas-ruled territory in a bid to halt Palestinian rocket fire and destroy a vast network of cross-border tunnels used by militants to stage attacks.
Gaza militants have fired close to 2,500 rockets at Israel since July 8, exposing most of Israel's population to an indiscriminate threat that has killed three civilians.
A Palestinian official said more than 1,000 Palestinians have been killed over the past 18 days. Israel says it is doing its utmost to prevent civilian casualties and blames Hamas for putting them in harm's way. Israel has lost 40 soldiers and two civilians. A Thai worker in Israel also has been killed.
Israeli Defense Minister Moshe Yaalon said Friday that Israel's military would continue to strike Hamas hard.
"At the end of the operation, Hamas will have to think very hard if it is worth it to taunt us in the future," Yaalon was quoted as telling soldiers manning an Iron Dome anti-missile battery. "You need to be ready for the possibility that very soon we will order the military to significantly broaden ground activity in Gaza."
The Associated Press contributed to this report.