On Monday, Israeli media reported that four hostages had been released from the Gaza Strip through the mediation of Qatar and Egypt.
"It's a very, very difficult negotiation that we've been dealing with," the top Qatari diplomat told UK media.
The negotiations are complicated by the fact that Israel and Palestine have "zero confidence in each other," he specified.
Qatar's main goal is to reach out to the parties, Al-Khulaifi said, adding that his country remained committed to the purpose despite various difficulties.
"If the mediator wants to perform its task in the best way possible as a state, then we need to reach a period of calm. We need to reach a period where we can speak logically to both sides and come up with positive initiatives," he added.
Meanwhile, Iranian Foreign Minister Hossein Amirabdollahian said at the UN General Assembly meeting that his country was also ready to take part in the efforts to release hostages. He stressed it was the international community's responsibility to free "6,000 Palestinian hostages" as well.