Italy, which holds the rotating presidency of the G20 forum of global economic powers, wants to call a meeting of its heads of state and government on Afghanistan as soon as possible.
The idea is to widen the global discussion on the crisis to countries including Russia and China.
China, a G20 member, may be set to play a bigger role in Afghanistan after the Taliban swept to power last month and Western forces withdrew.
For Beijing, a stable and cooperative administration in Kabul would pave the way for an expansion of its overseas infrastructure drive, analysts say.
The Taliban, meanwhile, may consider China a crucial source of investment and economic support.
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On Friday, a Taliban spokesman said Beijing had promised to increase humanitarian aid to the war-ravaged country.
Italy's Foreign Minister Luigi Di Maio said Tuesday that the ministry was working to "verify the conditions, modalities and timetable" for holding such a summit.