The UK says Israel should "stop and think seriously", the US wants to see a credible plan for civilians - but Israeli Prime Minister Benjamin Netanyahu insists an offensive in Rafah is needed to defeat Hamas.
As Israel rescued two hostages in the southern city, dozens were killed in the airstrikes that accompanied the operation.
There are now more than a million people in the city - with the UN agency for Palestinian refugees saying conditions are getting worse.
So can Israel be convinced to pause any ground offensive?
On this Sky News Daily, Leah Boleto speaks to our correspondent in Jerusalem, Diana Magnay, and defence and security analyst Professor Michael Clarke.
Senior podcast producer: Annie Joyce
Editor: Paul Stanworth
