"The forum has been supportive of this and we are hopeful that it [talks] restarts as soon as possible ... If you look at the joint statement it says very categorically [that the talks should be renewed] and of course the US side was part of it [joint statement]," the senior diplomat, who headed the Pakistani delegation, said.
US President Donald Trump broke off in September after a US soldier was killed in a Taliban-claimed bomb blast in Kabul. The Pakistani diplomat said it would only be natural for the US-Taliban talks to continue after so much understanding had been reached and "a lot of effort has been put in it."
"There is a general hope that it needs to be restarted because the progress that has been achieved after painstaking efforts by the two sides - the US and the Taliban - in nine rounds of talks is something very important," Aejaz said.
He added that the four participants of Moscow talks had reaffirmed their commitment to a peaceful solution for the decades-old conflict in Afghanistan.
"I can say that there is consensus among all the four parties that the only way is a peaceful solution and there is a need to expedite the efforts to reach it early rather than late," Muhemmed Aejaz said.
According to Muhemmed Aejaz, Pakistan, China, Russia and the United States agreed on Friday to reconvene for Afghan talks at a later date.
"I think that the joint statement concludes with this intention and this desire that the next round will be held, and as is the practice we agree on the venue and the date mutually through diplomatic channels. So, yes, it remains a very important forum and it will keep meeting as the need be," the senior diplomat, who headed the Pakistani delegation, said.
Moscow has hosted several rounds of consultations on Afghan peace in past years. The recent round was attended by the US special envoy for Afghanistan, Zalmay Khalilzad, who headed the US delegation to Doha for meetings with the Qatar-based political office of the Taliban movement.