Western nations are scrambling to get their citizens out of Kabul airport ahead of an August 31 deadline, along with Afghan nationals flagged as eligible to go.

Italy's foreign minister said it had evacuated close to 5,000 Afghan citizens in recent days, speaking at Rome's Fiumicino airport as the last Italian aircraft from Kabul landed with 58 more Afghan citizens on board.

"We are the EU country taking in the biggest number of Afghan evacuees," Luigi Di Maio said on Saturday.

The US, Britain and Germany are leading in terms of the number of people airlifted out of the country. Around 4,000 Afghans were among the evacuees taken in by Germany, while Italy has evacuated 4,900 Afghan citizens.

But Di Maio said it is still hoping to fly more Afghans out with the help of the United Nations, NGOs and other countries after the August 31 deadline.

"There are still so many Afghan nationals waiting to be evacuated, and we can no longer do that with the airlift," the minister said.

He added that "a second, more difficult phase" of the evacuations process would now commence.

"Our imperative will be not to abandon the Afghan people, not to abandon Afghan women, or young Afghans and all those who over all these years have shown a great desire for evolution, for change," Di Maio said.

More than 5,000 people remain inside Kabul airport awaiting evacuation, with just days to go before the final pull-out.

About 109,000 people have been flown out of the country since August 14, the day before the Taliban swept to power, according to the US government.

Twin suicide bombs on Friday claimed by a local affiliate of the Islamic State scuppered the already chaotic operation, killing scores of civilians and 13 American troops crowded around one of the airport's main access gates.