Mediators have made contact with the head of Hamas's military wing in Gaza, who has indicated he does not agree to the new US ceasefire plan, the BBC understands.
Izz al-Din al-Haddad is thought to believe the plan was designed to finish Hamas, whether the group accepts it or not, and so is determined to fight on.
US President Donald Trump's 20-point framework to end the war - which has already been accepted by Israel - stipulates that Hamas disarm and have no future role in governing Gaza.
It is thought that some of Hamas's political leadership in Qatar are open to accepting it with adjustments - but have found their influence limited as they do not have control of the hostages held by the group.
There are believed to be 48 hostages still being held in the Palestinian territory by the armed group, only 20 of whom are thought to be alive.
Another stumbling block for some in Hamas is that the plan requires them to hand over all of the hostages over the first 72 hours of the ceasefire - giving away their only bargaining chip.
Even with Trump's guarantee that Israel would abide by the terms, there is a lack of trust within the group that Israel would not resume its military operations once it had received the hostages - particularly after it attempted to assassinate the Hamas leadership in Doha in an air strike last month, in defiance of the US.
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