Hamas rejected the US-led Board of Peace's disarmament plan for the terror group and asked the board to make modifications to it, a source told The Jerusalem Post on Wednesday.
The BoP's high representative, Nickolay Mladenov, and three other mediators were also present, the source added.
Separately, while speaking to the BBC, a senior Palestinian official familiar with the talks accused Mladenov of pro-Israel bias.
The official also accused Israel of not yet fulfilling its obligations of Phase I of the ceasefire deal, saying that Hamas would not participate in Phase II negotiations until Israel does so.
"We are waiting for Mladenov to provide a clear timetable for Israel to fulfill the remaining obligations of Phase I," a senior Hamas official told the BBC.
Israel, though, has withdrawn from populated areas of the Gaza Strip to positions east of the Yellow Line, has increased the amount of aid entering the area, and maintains that movement on the terror group's disarmament is needed before further progress can be made on its side.
The BoP's disarmament plan was first passed to Hamas during meetings in Cairo last month, following the Trump administration's Middle East envoy Steve Witkoff's announcement of Phase II in mid-January.
Hamas repeatedly insists it will not disarm
Demilitarizing the terror group was part of the ceasefire agreement, initially signed in October, but since then, Hamas has repeatedly said that it would not give up its weapons.
Still, this most recent rejection comes days after the BoP's deadline for Hamas to agree to the disarmament proposal expired. The deadline required the terror group to accept the plan by the end of last week.
Hamas had previously been dragging its feet in giving a response to the disarmament proposal. Shortly after the plan was handed over, Palestinian Islamic Jihad and other militant and terror factions discarded it outrigh, saying it prioritized disarmament over reconstruction.
James Genn contributed to this report.