President Barack Obama, speaking by phone Sunday with Israeli Prime Minister Benjamin Netanyahu, stressed the need for an immediate, unconditional humanitarian ceasefire in Gaza, the White House said.
Urging a permanent end to hostilities on the basis of the 2012 ceasefire agreement, Obama added that "ultimately, any lasting solution to the Israeli-Palestinian conflict must ensure the disarmament of terrorist groups and the demilitarization of Gaza."
Fighting subsided in Gaza earlier Sunday after Hamas Islamist militants said they backed a 24-hour humanitarian truce.
Hamas said it had endorsed a call by the United Nations for a pause in the fighting in light of the upcoming Muslim holiday of Eid al-Fitr, expected to start in the next couple of days.
Some firing of rockets continued after the time that Hamas had announced it would put its guns aside and Netanyahu questioned the validity of the truce.
Israeli artillery guns also fired barrages into the Gaza Strip, Israeli media reported, although the object of the fire was initially unclear.
"Hamas doesn't even accept its own ceasefire, it's continuing to fire at us as we speak," Netanyahu said in an interview with CNN, adding that Israel would "take whatever action is necessary to protect our people".
Nonetheless, Gaza Strip residents and Reuters witnesses said Israeli shelling and Hamas missile launches had slowly subsided through the afternoon, suggesting a de facto truce might be taking shape as international efforts to broker a permanent ceasefire appeared to flounder.
However, Israel's military has said it will need more time to destroy a warren of tunnels that criss-cross the Gaza border that it says is one of its main objectives.
Egypt had also destroyed 13 tunnels which crossed into its territory, an Egyptian general said on his Facebook page. It was "a continuation of the efforts by the armed forces in protecting the borders of the state from smugglers and terrorists," Brigadier General Mohamed Samir Abdulaziz Ghoneim said.
Israel and the Hamas Islamists who control Gaza had agreed to a 12-hour ceasefire on Saturday to allow Palestinians to stock up on supplies and retrieve bodies from under the rubble.
Netanyahu's cabinet voted to extend the truce until midnight on Sunday at the request of the United Nations, but called it off when Hamas launched rockets into Israel during the morning.
Palestinian medics said at least 10 people had died in the wave of subsequent strikes that swept Gaza, including a Christian woman, Jalila Faraj Ayyad, whose house in Gaza City was struck by an Israeli bomb.
Some 1,031 Palestinians, mainly civilians and including many children, have been killed in the 20-day conflict. A Gaza health ministry official issued revised figures of dead, saying that 30 fewer people than thought had died in the conflict.
Israel says 43 of its soldiers have died, along with three civilians killed by rocket and mortar fire out of the Mediterranean enclave.
Israel launched its Gaza offensive on July 8, saying its aim was to halt rocket attacks by Hamas and its allies.
After aerial and naval bombardment failed to quell the outgunned guerrillas, Israel poured ground forces into the Gaza Strip 10 days later, looking to knock out Hamas's rocket stores and destroy the vast network of tunnels.
The army says its drive to find and eliminate tunnels would continue through any temporary truce.
Diplomatic efforts led by U.S. Secretary of State John Kerry to end the 20-day conflict have shown little sign of progress. Israel and Hamas have set conditions that appear irreconcilable.
Hamas wants an end to the Israeli-Egyptian economic blockade of Gaza before agreeing to halt hostilities. Israel has signaled it could make concessions toward that end, but only if Gaza's militant groups are stripped of their weapons.