The money would be used to convince individual Taliban fighters who do not back al-Qaeda that they are better off on the government's side than fighting on the side of the Taliban.
Zalmay Rasoul, the incoming Afghan foreign minister, said the programme is targeted at Taliban members who are tired of fighting.
"Every war will finish some time, and we are targeting those people who are tired and sick of fighting," he told The Associated Press news agency on Wednesday.
The Taliban has dismissed the plan. In a statement released on Wednesday, the group said its fighters would not be swayed by financial incentives and demanded the withdrawal of foreign forces from the country.
"The London conference is in fact aimed at extending the invasion of Afghanistan by occupying forces ... [It] is just a waste of time," it said.
Several countries, including the United States, are said to be leading the proposal.
Al Jazeera's James Bays, reporting from London, said the policy of outreach to the Taliban indicates a "complete U-turn" from the policies of the past US administration.
However he said it is still unclear if the strategy will be successful.
"I'm told by reliable sources that the amount of money we're talking about is somewhere between $500m and a billion dollars over the next five years.
"That money will be used in different ways. Some money may go directly to Taliban fighters, but they're also going to change the conditions in the communities in those areas where people are fighting the government to try to persuade people to change sides.
"Part of it is to try to persuade the fighting force to change sides and the other part is to try and start some sort of dialogue with members of the Taliban to persuade some of them to join the political process."
Obstacles to reconciliation
Abdullah Abdullah, a former Afghan foreign minister and Karzai's challenger in the country's recent presidential election, said reconciliation should be an immediate priority but should start at the local level.
"The door has to remain open for national reconciliation," he told Al Jazeera.
"I believe it has to be a nationally debated and transparent programme under the realm of the constitution of Afghanistan."
But he said obstacles remain to implementing such a policy.
"I don't think the Taliban at this stage are willing to enter negotiations. Also, their association with terrorist organisations, like al-Qaeda - that's the main issue at the moment - and they are working like one organisation."
"So national reconciliation should be local, among those who are willing to join peaceful life. Also the main focus has to be on the people themselves, so the Taliban have no more recruits."
Meeting the opposition
Thursday's conference comes nearly a week after a meeting between Afghan government officials and members of an armed opposition group fighting alongside the Taliban.
Al Jazeera's David Chater, reporting from the Afghan capital, Kabul, said the talks were held with the group Hezb-e-Islami, in the Maldives islands, on January 23-24.
"Gulbuddin Hekmatyar [the group's leader] sent his son and two son-in-laws to the meeting," he said.
"They [government representatives and Hezb-e-Islami] decided to set up two delegations ... One will be headed by Hekmatyar's son and the other one will be headed by the deputy head of the peace and reconciliation commission.
"He will go and see President Karzai and Hekmatyar's son will go and see the Taliban."
Chater said a Taliban leader had been due to attend the meeting but dropped out in the last minute citing health reasons.