They jointly said that it would “only bring more death and suffering” and “threaten regional escalation”.
The US also said it opposed any assault on Rafah, where more than 1.5 million Palestinians are sheltering.
Israeli PM Benjamin Netanyahu said a date for the offensive had now been set but provided no details.
“Today I received a detailed report on the talks in Cairo, we are constantly working to achieve our goals, first and foremost the release of all our hostages and achieving a complete victory over Hamas,” he said on Monday.
“This victory requires entry into Rafah and the elimination of the terrorist battalions there. It will happen – there is a date.”
At the same time, Israeli Defence Minister Yoav Gallant suggested that now was the right time for a deal over hostages, six months into the war with Hamas.
His comments came as talks on a hostage-prisoner swap and ceasefire continued in Egypt’s capital Cairo.
The CIA Director, William Burns, is also attending the discussions. His presence underlines the growing pressure from the US – Israel’s main ally – for an agreement.
A senior Hamas official told Reuters news agency Israeli proposals had not met Hamas’s demands but the group said they would nevertheless be examined.
“There is no change in the position of the occupation [Israel] and therefore, there is nothing new in the Cairo talks,” the Hamas official, who asked not to be identified, said. “There is no progress yet.”
In a separate development on Monday, Israel reported a “record-breaking influx of aid trucks into Gaza, totalling 419”.
“We warn against the dangerous consequences of an Israeli offensive on Rafah,” Egyptian President Abdel Fattah al-Sisi, French President Emmanuel Macron and Jordan’s King Abdullah II said in a joint editorial published in several newspapers.
They also said a recent UN Security Council resolution calling for an immediate ceasefire and the release of all Hamas-held hostages must be “fully implemented without further delay”.
“The war in Gaza and the catastrophic humanitarian suffering it is causing must end now,” the three leaders said, urging a “massive increase” in aid for Gaza.
Egypt and Jordan – who both border Israel – are seen as key players in the war-torn Middle East region.
Hamas attacked southern Israeli border communities on 7 October, killing 1,200 people and taking more than 250 hostage.
Israel says that of 130 hostages still in Gaza, at least 34 are dead.
More than 33,000 Gazans, the majority of them civilians, have been killed during Israel’s offensive in Gaza since then, the Hamas-run health ministry says.
Gaza is said to be on the brink of famine, with Oxfam reporting that 300,000 people trapped in the north have lived since January on an average of 245 calories a day.
Israel has denied impeding the entry of aid or its distribution inside Gaza, and has accused UN agencies on the ground of failing to get the aid that is allowed in to the people who need it.