The BBC understands that mediators have made contact with the head of Hamas's military wing in Gaza, who indicated he does not agree to new US ceasefire plan.
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 must disarm and has 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 remaining hostages, 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 within 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.
Some Hamas leaders are also thought to object to the deployment by the US and Arab states of what the plan describes as a temporary International Stabilisation Force to Gaza, which they view as a new form of occupation.
Additionally, a map of the proposed phased Israeli troop withdrawals from Gaza shared by the Trump administration shows what it refers to as a security buffer zone along Gaza's borders with Egypt and Israel, which is likely to be contentious.
Further, since agreeing to the plan on Monday evening, Israeli Prime Minister Benjamin Netanyahu has appeared to push back on several of the terms, indicating that Israeli military presence will remain in parts of Gaza.
Hamas has previously stated it will not disarm until a sovereign Palestinian state is established. The Israeli military launched a campaign in Gaza in response to the Hamas-led attack on southern Israel on October 7, 2023, resulting in significant casualties and escalating tensions in the region.