Israel has said it plans to seize the city, where about a million Palestinians have been sheltering, as part of its declared aim of eliminating the militant group Hamas, and has intensified attacks on what it has called Hamas' last bastion.
The group's political leadership, which has engaged in on-and-off negotiations on a possible ceasefire and hostage release deal, was targeted by Israel in an air strike in Doha on Tuesday - an attack that drew widespread condemnation.
Qatar will host an emergency Arab-Islamic summit on Monday to discuss the next moves.
Rubio said Washington wanted to talk about how to free the 48 hostages still held by Hamas in Gaza - 20 of whom are believed to be alive - and how to rebuild the coastal strip.
"What's happened, has happened," he said.
"We're gonna meet with them (the Israeli leadership). We're gonna talk about what the future holds," Rubio said before heading to Israel, where he will stay until Tuesday.
Rubio visited the Western Wall Jewish prayer site in Jerusalem on Sunday with Prime Minister Benjamin Netanyahu and will hold talks with him during the visit.
US officials described Tuesday's strike on the territory of a close US ally as a unilateral escalation that did not serve American or Israeli interests.
Rubio and US President Donald Trump both met Qatar's Prime Minister Mohammed bin Abdulrahman Al-Thani on Friday.
Netanyahu signed an agreement on Thursday to push ahead with a settlement expansion plan that would cut across West Bank land that the Palestinians seek for a state - a move the United Arab Emirates warned would undermine the US-brokered Abraham accords that normalised UAE relations with Israel.
Aid agencies say an Israeli takeover of Gaza City would be catastrophic for a population already facing widespread malnutrition.
Two more Palestinians have died of malnutrition and starvation in Gaza in the past 24 hours, the territory's health ministry said on Sunday, raising deaths from such causes to at least 422 people, including 145 children.
Israel, which blocked all food from entering Gaza for 11 weeks earlier this year, has been allowing more aid into the enclave since late July to prevent further food shortages, though the United Nations says far more is needed.
It says it wants civilians to leave Gaza City before it sends more ground forces in.
Tens of thousands of people are estimated to have left but hundreds of thousands remain in the area.
Hamas has called on people not to leave.
Israeli army forces have been operating inside at least four eastern suburbs for weeks, turning most of at least three of them into wastelands.
It is closing in on the centre and the western areas of the territory, where most of the displaced people are taking shelter.
Many are reluctant to leave, saying there is not enough space or safety in the south, where Israel has told them to go to what it has designated as a humanitarian zone.
Israel said it had completed five waves of air strikes on Gaza City in the past week, targeting more than 500 sites, including Hamas reconnaissance and sniper sites, buildings containing tunnel openings and weapons depots.
Local officials, who do not distinguish between militant and civilian casualties, say at least 40 people were killed by Israeli fire across the enclave - 28 in Gaza City alone.
Hamas said Israeli forces have destroyed at least 1600 residential buildings and 13,000 tents since August 11.
Israel's almost two-year-long campaign against Hamas has killed more than 64,000 people in Gaza, according to local authorities.
It was prompted by Hamas's October 7, 2023, attack on Israel that killed 1200 people and the kidnapping of 251 hostages, according to Israeli figures.
