Italy, which holds the rotating presidency of the G20, is still pushing for a special meeting on Afghanistan as its last evacuation flight has left Kabul.
Italy's last airlift flight, carried out by a military C-130 plane, is expected to land in Rome on Saturday, bringing back "all the Italians who asked to be repatriated", Foreign Minister Luigi Di Maio said on Friday.
He confirmed that some 4,900 Afghan nationals who wanted to leave following the Taliban takeover of the war-ton nation have been evacuated by Italian forces during the operation, reports Xinhua news agency.
At a joint press conference held here on Friday after meeting with his Russian counterpart Sergei Lavrov, Di Maio reiterated the country's plan to hold an extraordinary G20 summit on Afghanistan in September to outline a global strategy.
"Afghanistan has been at the core of our talks today... in this context, we see the dialogue with Russia as essential," he explained.
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He added that Italy's push to organise a special G20 meeting on Afghanistan stemmed from the belief that only "a comprehensive, coherent and shared action can be effective with the new authorities in Kabul".
"We believe Moscow is a key player in dealing with the current crisis and, in a longer perspective, in achieving a unified international approach.
"We deem that the G20 could be the right platform for a common management of the crisis, which has to be shared with the countries that will bear the largest migrant influx, that is the neighbouring countries," Di Maio added.
Lavrov, who paid a two-day visit in Italy, said that the security of Afghanistan's neighbouring countries should be a key priority after all evacuation operations are completed.
He also urged for speeding up support for the Afghan people in order to facilitate the formation of an inclusive executive as soon as possible.
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"Common solutions are never easy and, in our opinion, the most important thing in the current situation is the security of our borders," said the top Russian diplomat, who also discussed the issue with Italian Prime Minister Mario Draghi earlier in the day.
Russia is ready to discuss the proposal of the G20 special summit, but "we want to better understand what role our Western partners would see for Russia in the G20 context", Lavrov said.