State Minister for Peace Affairs Abdul Salam Rahimi said on Saturday it was hoped that direct talks with the Taliban would be held in the next two weeks in an unidentified European country.
The government would be represented by a 15-member delegation, he said.
But Suhail Shaheen, a spokesman for the Taliban's political office in Qatar, denied that, saying talks with the Afghan government would only come after a deal had been struck with the United States on the departure of its forces.
Taliban-Kabul direct talks likely next month
"Intra-Afghan talks will start only after a foreign force withdrawal is announced," Shaheen said.
The US special envoy for peace in Afghanistan, Zalmay Khalilzad, said after Rahimi had made his announcement that talks between the Taliban and Afghans would happen after the United States "concludes its own agreement" with the Taliban.
Khalilzad has held several rounds of direct talks with Taliban officials in Qatar since late last year with the focus on a Taliban demand for the withdrawal of US and other foreign forces and a US demand the Taliban guarantee that Afghanistan will not be used as a base for terrorism.
Two other main issues in the peace process are a ceasefire and talks between the rival Afghan sides, or inter-Afghan talks, as they are known.
But the Taliban have refused to talk to the government of President Ashraf Ghani, denouncing it as a US puppet, and fighting has seen no let-up.
That has led to some concern in Afghanistan that the United States might strike a deal to allow the United States to pull out of an 18-year war that President Donald Trump is impatient to end, leaving the Afghan government to battle on alone.
Afghan Taliban say ready to meet PM Imran
Khalilzad has in recent days been holding meetings with Ghani, opposition leaders, diplomats and civil society members in Kabul before heading to Qatar for the next round of talks with the Taliban.
Two sources privy to the talks said the United States and the Taliban were expected to sign a memorandum of understanding this week to firm up a plan for the withdrawal of foreign troops and for a Taliban pledge to stop militant plotting from Afghan soil.
Khalilzad said on Twitter that after the US concludes its agreements, intra-Afghan negotiations would take place between the Taliban and "an inclusive and effective national negotiating team consisting of senior government officials, key political party representatives, civil society and women".
About 20,000 foreign troops, most of them American, are in Afghanistan as part of a US-led NATO mission to train, assist
and advise Afghan forces. Some US forces carry out counter-terrorism operations.
Afghan 'peace is coming': Ghani
Afghanistan's president marked the official start of the country's election season on Sunday by insisting "peace is coming" and that pivotal talks with the Taliban would take place.
Ashraf Ghani is hoping to fend off challenges from 17 other candidates to score a second term at twice-postponed presidential elections now slated for September 28.
"Peace is coming, and the negotiations will take place," Ghani said at a rally marking the start of two months of campaigning.
Such a development could be crucial, as the Taliban -- who now control or influence about half of Afghanistan -- have so far refused to speak to Ghani's government, as they consider the Kabul administration illegitimate.
War aside, the country faces a host of major issues ahead of the election, including rocketing crime, a lacklustre economy, soaring unemployment, and crumbling infrastructure.
Voters are despondent about the prospects of a fair election, and many worry about a repeat of the sort of violent attacks on previous polls by the Taliban and other insurgent groups trying to undermine Afghanistan's fragile democracy.
Ghani insisted this year's election would be "clean".
In Kabul, security forces fanned out across the city as leading candidates held rallies.
Campaign posters of Ghani, his main rival Abdullah Abdullah, and other candidates were unveiled across the country.
Abdullah is currently serving as the president's chief executive under an awkward power-sharing arrangement brokered by the US after the fraud-tinged 2014 election.
"It is our national and religious duty to take advantage of any opportunities for peace," Abdullah told a campaign rally.
One crucial issue is that the elections happen at all: they were postponed twice this year and further delays could lead to more unrest.
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