UK Foreign Secretary David Cameron said “over half of Gaza’s population are sheltering in the area”, while Dutch FM Hanke Bruins Slot said there could be “many civilian casualties”.
Saudi Arabia warned of “very serious repercussions” if Rafah was stormed.
Gaza’s Hamas rulers said there could be “tens of thousands” of casualties.
Israel launched its operations in the Palestinian enclave after more than 1,200 people were killed in southern Israel on 7 October by Hamas gunmen.
On Sunday the Hamas-run health ministry in Gaza said 112 more Palestinians had been killed by the Israeli military over the previous day, bringing the overall death toll to more than 28,100 and more than 67,500 injured.
Many Gazans have ended up in Rafah having been forced to flee their homes elsewhere at least once.
Saturday’s warnings came a day after Israeli Prime Minister Benjamin Netanyahu ordered his military to prepare to evacuate civilians from the city ahead of an expanded offensive against Hamas.
“It is impossible to achieve the goal of the war without eliminating Hamas, and by leaving four Hamas battalions in Rafah. It is clear that intense activity in Rafah requires that civilians evacuate the areas of combat,” Mr Netanyahu’s office said.
The prime minister also rejected Hamas’s latest proposed ceasefire terms.
The US has already warned Israel that an invasion of Rafah as part of its assault on Gaza would be a “disaster”, while the EU and the UN both expressed their own concerns.
Aid groups say it is not possible to evacuate everyone from the city on the border with Egypt.
UN humanitarian co-ordinator Jamie McGoldrick, who has just been to Gaza to assess the situation, told the BBC’s Barbara Plett Usher that people in Rafah would have “nowhere to go” if Israeli troops launched their offensive.
“The safe areas that were declared are no longer safe. And if these people have to move – where can they move? We are really fearful of the horrific nature of where we are could only ever get worse,” he said.
Some 1.5 million Palestinians are believed to be in Rafah, seeking refuge from Israeli combat operations in the rest of the Gaza Strip. Most of them are living in tents.