US President Donald Trump threatened Hamas on Tuesday with "fast, furious, brutal force" if it does not "do what is right" as he pushes for the next, more complex, stage of a Gaza ceasefire that has already been repeatedly tested.
Increasing the pressure on the Palestinian militant group, Trump said in a social media post that numerous U.S. allies had said they would welcome the chance to go into Gaza and hit Hamas, but he had told them and Israel "not yet".
This comes as Vice President JD Vance arrived on Tuesday to meet Israeli Prime Minister Benjamin Netanyahu on Wednesday for talks Israel said would focus on security challenges and political opportunities.
Israel and Hamas have accused each other of repeated breaches of the truce since it was signed eight days ago, with flashes of violence and recriminations over the pace of returning hostage bodies, bringing in aid and opening borders.
Speaking to Egyptian television late on Monday, Hayya reaffirmed the group's compliance with the truce and said it would fulfil its obligations in the first phase, including returning more bodies of hostages.
"Let their (hostages) bodies return to their families, and let the bodies of our martyrs return to their families to be buried in dignity," he said.
Hamas released another hostage body late on Monday and said it would hand over two more late on Tuesday. That would leave another 13 bodies in Gaza. Israel believes Hamas could still return more bodies soon but has recognised that some remains would likely need a slower, more complex, process of location and retrieval.
Israel handed back another 15 Palestinian bodies on Tuesday, local health authorities said, taking the total it has returned to Gaza to 165.
Inside the enclave on Tuesday, more aid was flowing in through two Israeli-controlled crossings, Palestinian and UN officials said.
However, with Gaza residents facing catastrophic conditions, aid agencies have said far more needs to be brought in.
The UN World Food Programme said supplies were ramping up but fell far short of its daily target of 2,000 tons, saying this was because only two crossings into Gaza were open. It said none had reached the famine-hit north of Gaza yet.
Violence in Gaza since the truce has mostly focused been around the "yellow line" demarcating Israel's military pullback. On Tuesday Israel's public Kan radio reported troops had killed a person crossing the line and advancing towards them.
Palestinians near the line, running across devastated areas close to major cities, have said it is not clearly marked and hard to know where the exclusion zone begins. Israeli bulldozers began placing yellow concrete blocks along the route on Monday.
The Gaza health ministry said on Tuesday at least seven Palestinians were killed by Israeli fire across the enclave over the previous 24 hours, bringing to 68,229 the total number killed since the war began.
Hamas' October 7th, 2023, attack on Israel that triggered the war killed around 1,200 people according to Israeli tallies, with another 251 dragged into Gaza as hostages.