Israel is intensifying military operations in one of the last Hamas strongholds in Gaza, as the sides stake out positions before ceasefire negotiations proposed by US President Donald Trump.

U.S. President Donald Trump says Israel has agreed on terms for a new 60-day ceasefire with Hamas and that Washington would work with both sides during that time to try to end more than 20 months of war in Gaza.

Hamas said it was studying new ceasefire offers received from mediators Egypt and Qatar but that it aimed to reach an agreement that would ensure an end to the war and an Israeli pullout from Gaza.