Israel has taken control of the vital Rafah border crossing between Gaza and Egypt after launching air strikes.
Israel carried out the next stage of its offensive while the prospects for a ceasefire deal hung in the balance.
The Palestinian militant group Hamas said late on Monday it had agreed to a ceasefire proposal from mediators seven months into the war that has pushed more than a million Gazans into the south of the enclave.
Israel said the terms did not meet its demands and launched a military operation in Rafah.
Israeli tanks played a key part of the military operation
REUTERS
Israeli tanks and planes pounded several areas and houses in Rafah overnight
REUTERS
Israeli tanks and planes pounded several areas and houses in Rafah overnight, killing 20 Palestinians and wounding several others in strikes that hit at least four houses, Palestinian health officials said.
"The Israeli occupation has sentenced the residents of the Strip to death after closure of the Rafah border crossing," said Hisham Edwan, spokesman for the Gaza Border Crossing Authority. It also condemned to death cancer patients due to the collapse of the healthcare system, he added.
Israel has been threatening to launch a major incursion in Rafah, which it says harbours thousands of Hamas fighters and potentially dozens of hostages. Victory is impossible without taking Rafah, it says.
A Gaza border authority spokesperson told Reuters the Rafah crossing, a major route for aid into the devastated enclave, was closed because of the presence of Israeli tanks. Israel's Army Radio had earlier announced its forces were there.
The United States has been pressing Israel not to launch a military campaign in Rafah until it had drawn up a humanitarian plan for the Palestinians sheltering there, which Washington says it has yet to see.
Israel said the vast majority of people had been evacuated from the area of military operations.
Israel said the vast majority of people had been evacuated from the area of military operations
REUTERS
Instructed by Arabic text messages, phone calls and flyers to move to what the Israeli military called an "expanded humanitarian zone" around 20 km (12 miles) away, some Palestinian families began trundling away in chilly spring rain.
The attack came after Hamas said in a brief statement that its chief, Ismail Haniyeh, had informed Qatari and Egyptian mediators the group accepted their proposal for a ceasefire.
Israeli Prime Minister Benjamin Netanyahu's office said later the truce proposal fell short of Israel's demands but Israel would send a delegation to meet with negotiators to try to reach an agreement.
Qatar's foreign ministry said its delegation will head to Cairo on Tuesday to resume indirect negotiations between Israel and Hamas.
In a statement, Netanyahu's office said his war cabinet approved continuing an operation in Rafah. Jordan's Foreign Minister Ayman Safadi said on social media that Netanyahu was jeopardising a ceasefire by bombing Rafah.
An Israeli official, speaking on condition of anonymity, said the proposal that Hamas approved was a watered-down version of an Egyptian offer and included elements Israel could not accept.
"This would appear to be a ruse intended to make Israel look like the side refusing a deal," said the Israeli official.
Another official briefed on the agreement said Hamas had agreed to the phased ceasefire and hostage release deal Israel proposed on April 27 with only minor changes that did not affect the main parts of the proposal.
US State Department spokesman Matthew Miller said Washington would discuss the Hamas response with its allies in the coming hours, and a deal was "absolutely achievable".
Any truce would be the first pause in fighting since a week-long ceasefire in November, during which Hamas freed around half of the hostages.
Since then, all efforts to reach a new truce have foundered over Hamas' refusal to free more hostages without a promise of a permanent end to the conflict, and Israel's insistence that it would discuss only a temporary pause.
