The Prime Minister will chair a virtual meeting with the other members on Tuesday afternoon where he will urge Britain's international partners to match the UK's commitments on aid.
Mr Johnson and his fellow leaders are also expected to reiterate their commitment to safeguarding the gains made in Afghanistan over the last 20 years, despite the Taliban takeover.
He said: “Our first priority is to complete the evacuation of our citizens and those Afghans who have assisted our efforts over the last 20 years – but as we look ahead to the next phase, it’s vital we come together as an international community and agree a joint approach for the longer term.
“That’s why I’ve called an emergency meeting of the G7 - to coordinate our response to the immediate crisis, to reaffirm our commitment to the Afghan people, and to ask our international partners to match the UK’s commitments to support those in need.
“Together with our partners and allies, we will continue to use every humanitarian and diplomatic lever to safeguard human rights and protect the gains made over the last two decades. The Taliban will be judged by their deeds and not their words.”
Discussions are also set to cover ongoing collaboration on evacuation efforts at Kabul airport and longer-term work to secure a more stable future for Afghanistan and ensure any new government is inclusive and abides by its international obligations.
It comes with Mr Johnson also trying to convince the US president to delay the withdrawal of forces from Kabul airport during a summit of G7 leaders.
The Taliban have taken Afghanistan in a little over a week, and warned any attempt to delay the full withdrawal past August 31 would “provoke a reaction”.
Speaking to reporters in Fort George, near Inverness, Defence Secretary Ben Wallace warned the US leaving took away the “framework” to get people out.
He explained: “I don’t think there is any likelihood of staying on after the United States. If their timetable extends even by a day or two that will give us a day or two more to evacuate people.
“Because we are really down to hours now, not weeks, and we have to make sure we exploit every minute to get people out.”
First Minister Nicola Sturgeon called for discussions over how many refugees Scotland take to “intensify”.
She said: “There’s been some correspondence between myself and Boris Johnson and between my ministers and UK Government ministers.
“We don’t yet have a number that Scotland will welcome here, but I hope to get to that as soon as practically possible.
“There’s lots of work to be done – lots of practical arrangements – but as well as living up to our responsibility to give refuge to people fleeing horrific circumstances like those seen in Afghanistan right now, we stand to gain a lot as well.”
The Ministry of Defence confirmed that 5,725 people have been repatriated since rescue efforts began on August 13, with 3,100 of them Afghan individuals and their families.