Israel says it wants to root out Hamas fighters holed up in Rafah and rescue hostages it says are being held in the area, but its assault has worsened the plight of civilians and caused an international outcry.
On Sunday, Israeli strikes killed at least five Palestinians in Rafah, according to local medical services.
Israeli tanks have probed around the edges of the city, close to the main southern crossing point into Egypt, but have not yet entered the city in force.
Following the rocket salvo, Israel's hardline public security minister Itamar Ben Gvir - who is not part of Israel's war cabinet - urged the army to hit Rafah harder.
"Rafah with full force," he posted on X.
Nearly 36,000 Palestinians have been killed in Israel's offensive, Gaza's health ministry says. Israel launched the operation after Hamas-led militants attacked southern Israeli communities on Oct. 7, killing around 1,200 people and seizing more than 250 hostages, according to Israeli tallies.
Fighting also continued on Sunday in the northern Gaza area of Jabaliya, a heavily built up area which saw weeks of intense combat earlier in the war. During one raid, the military said it found a weapons storage site with dozens of rocket parts and weapons located in a school.
It denied statements by Hamas that Palestinian fighters had abducted an Israeli soldier.
TRUCE TALKS
Efforts to agree a halt to the fighting and return more than 100 hostages still held in Gaza have been blocked for weeks but there were some signs of movement following meetings between Israeli and US intelligence officials and the prime minister of Qatar.
An official with knowledge of the matter said a decision had been taken to resume the talks this week based on new proposals from Egyptian and Qatari mediators, and with "active U.S. involvement."
However, a Hamas official played down the report, telling Reuters: "It is not true."
Izzat El-Reshiq, a senior Hamas official in exile, said the group had not received anything from the mediators on new dates for the resumption of talks as had been reported by Israeli media.
Reshiq restated Hamas's demands, which include: "Ending the aggression completely and permanently, in all of Gaza Strip, not only Rafah".
While Israel is seeking the return of hostages, Prime Minister Benjamin Netanyahu has repeatedly said the war will not end until Hamas is eliminated.
AID TRUCKS ENTER GAZA
Israel has faced calls to get more aid into Gaza after more than seven months of a war that has caused widespread destruction and hunger in the enclave.
Israel prepared on Sunday to allow around 200 aid trucks into Gaza through Kerem Shalom at the southeastern edge of the Palestinian enclave, bypassing the main Rafah crossing that has been blocked for weeks.
It follows an agreement between U.S. President Joe Biden and Egyptian President Abdel Fattah al-Sisi on Friday to temporarily send aid via the crossing.
Khaled Zayed, an official from the Egyptian Red Crescent, told Reuters 200 trucks of aid, including four fuel trucks, were expected to enter on Sunday through the Kerem Shalom crossing.
Egypt's state-affiliated Al Qahera News TV shared a video on social media platform X, showing what it said were aid trucks as they entered Kerem Shalom, which before the conflict was the main commercial crossing station between Israel, Egypt and Gaza.
The Rafah crossing has been shut for almost three weeks, since Israel took control of the Palestinian side of the crossing as it stepped up its offensive in the area on May 6.
Egypt has been increasingly alarmed at the prospect of large numbers of Palestinians entering its territory from Gaza and has refused to open its side of the Rafah crossing.
Israel has said it is not restricting aid flows and has opened up new crossing points in the north as well as cooperating with the United States, which has built a temporary floating pier for aid deliveries.