Israeli airstrikes have hit around 40 targets across the Gaza Strip over the past day, the military says, hours after Hamas rejected an Israeli ceasefire offer that it said fell short of its demand to agree a full end to the war.
Last month, the Israeli military broke off a two-month truce that had largely halted fighting in Gaza and has since pushed in from the north and south, seizing almost a third of the enclave as it seeks to pressure Hamas into agreeing to release hostages and disarm.
The military said troops were operating in the Shabura and Tel Al-Sultan areas near the southern city of Rafah, as well as in northern Gaza, where it has taken control of large areas east of Gaza City.
Egyptian mediators have been trying to revive the January ceasefire deal, which broke down when Israel resumed airstrikes and sent ground troops back into Gaza, but there has been little sign that the two sides have moved closer on fundamental issues.
Late on Thursday, Khalil Al-Hayya, Hamas' Gaza chief, said the movement was willing to swap all remaining 59 hostages for Palestinians jailed in Israel in return for an end to the war and reconstruction of Gaza.
But he dismissed an Israeli offer, which includes a demand that Hamas lay down its arms, as imposing "impossible conditions".
Israel has not responded formally to Al-Hayya's comments but ministers have said repeatedly that Hamas must be disarmed completely and can play no role in the future governance of Gaza. The ceasefire offer it made through Egyptian mediators includes talks on a final settlement to the war but no firm agreement.
Defence Minister Israel Katz also said this week that troops would remain in the buffer zone around the border that now extends deep into Gaza and cuts the enclave in two, even after any settlement.