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Hamas has said that any resumption of ceasefire talks about the conflict in Gaza should be based on previous plans rather than holding new rounds of negotiations.
Last week, international mediators from Qatar, Egypt and the US urged Israel and Hamas to attend negotiations on a ceasefire and hostage release deal on 15 August.
Israel responded on Thursday, saying it would send a team of negotiators to take part in the meeting. Negotiations faltered last month, after new terms were introduced to the framework presented by US President Joe Biden in May.
On Monday, the leaders of the UK, France and Germany issued a joint call for talks to resume, saying there "can be no further delay."
UK Prime Minister Sir Keir Starmer, French President Emmanuel Macron and German Chancellor Olaf Scholz echoed the mediators' call for ceasefire talks to resume in a joint statement.
"We agree that there can be no further delay", the statement said.
"We have been working with all parties to prevent escalation and will spare no effort to reduce tensions and find a path to stability."
The countries also called for the de-escalation of tensions in the Middle East - which have risen since the assassination of senior members of Hamas and Hezbollah.
US Defence Secretary Lloyd Austin confirmed on Sunday night that he had ordered the deployment of a guided missile submarine to the Middle East which will join the aircraft carrier USS Abraham Lincoln, which is heading to the region.
Iran previously said it will respond to the killing of Hamas leader Ismail Haniyeh at the “right time” in the "appropriate" manner and that the US bears responsibility for his death because of its support of Israel.
Aftermath of Israeli strike on Gaza City school
In a statement about the ceasefire talks, Hamas responded to pressure from mediators by calling for a plan to be drawn up based on Mr Biden's "vision" from May - essentially agreeing to resume negotiations from the point where they stopped rather than on any new initiative.
"The mediators should enforce this on the occupation (Israel) instead of pursuing further rounds of negotiations or new proposals that would provide cover for the occupation's aggression and grant it more time to continue its genocide against our people," the Hamas statement said.
Sources told the BBC that the introduction of new Israeli conditions - that displaced Palestinians should be screened as they return to the north of Gaza, as well as the question of control of the Philadelphi corridor that borders Egypt - had been sticking points.
The BBC understands that Hamas is open to resuming talks at the point prior to which the new conditions were introduced.
On Sunday, the Israeli military ordered thousands of Palestinians in Khan Younis, southern Gaza, to relocate to what it has designated "humanitarian zones".
The relocation order followed an Israeli air strike against a school building in Gaza on Saturday, which killed more than 70 people according to a local hospital director.
Fadl Naeem, head of al-Ahli Hospital where many of the casualties were taken, said around 70 victims were identified in the hours after the strike - with the remains of many others so badly disfigured that identification was difficult.
A spokesman for the Israel Defense Forces (IDF) said the school "served as an active Hamas and Islamic Jihad military facility", which Hamas denies.
IDF spokesman Rear Adm Daniel Hagari said “various intelligence indications” suggest a “high probability” that the commander of Islamic Jihad’s Central Camps Brigade, Ashraf Juda, was at al-Taba’een school school when it was struck.
He said it is not yet clear whether the commander was killed in the attack.
The BBC cannot independently verify casualty figures from either side.
Israel claims that Hamas is using civilian infrastructure to plan and carry out attacks, and that is why it has been targeting hospitals and schools - sites protected under international law.
Hamas has consistently denied the accusations.
Hamas-led gunmen killed about 1,200 people in an attack on Israel on 7 October, taking 251 others back to Gaza as hostages.
That attack triggered a massive Israeli military offensive against Gaza and the current war.
More than 39,790 Palestinians have been killed in the Israeli campaign, according to Gaza's Hamas-run health ministry.