Kabulov's remarks came a day after U.S. President Donald Trump said that peace talks with the Taliban are "dead" after cancelling a planned meeting outside of the nation's capital, in retaliation for recent Taliban attack in Kabul, which killed a dozen people, including a U.S. service member.
A plume of smoke rose over Kabul just after midnight and sirens could be heard.
Several called the timing unfortunate but the idea of talks worthwhile, a potential path toward peace for Afghans and Americans tired of Washington's longest war.
Two Taliban auto bombs shook Kabul last week, killing several civilians and two members of the North Atlantic Treaty Organisation mission.
Peace talks had been meant to debate the withdrawal of United States troops from Afghanistan, a prerequisite for peace within the nation.More news: Cubs' Baez dealing with hairline fracture in thumb
"We had two ways to end the occupation in Afghanistan, one was fighting, the other was talks and negotiations", Zabihullah Mujahid, a Taliban spokesman, told the Agence France-Presse (AFP) news agency.
'If Trump desires to cease talks, we are going to take the primary manner and they'll quickly remorse it'.
The assault came days after the top US peace negotiator, Zalmay Khalilzad, proclaimed that almost a year of peace negotiations with the Taliban had yielded a deal "in principle".
A US-led invasion of Afghanistan shortly after the 2001 attack toppled the Taleban, who had harboured Osama bin Laden, the Al-Qaeda leader and attacks mastermind.
It is widely thought that Trump has been pushing for a withdrawal of U.S. troops in time for his 2020 reelection bid.More news: Stampede during religious event in Iraq leaves at least 31 dead
In Afghanistan, the USA military is also fighting to prevent the South Asian country from becoming a haven for jihadis seeking to attack the United States.
Last week's bombings included an attack late Monday which killed 16 and injured 100, mostly civilians, and an attack Thursday which killed two soldiers and ten civilians.
Tallon wants USA troops home, and she really wants the US government to do more to probe allegations, which she and others have raised in a lawsuit, that Saudi government employees knowingly assisting the hijacking plot.
The U.N. envoy said opportunities for peace over the past year "created hope, but also fear for many", and made clear that the conflict can only be resolved by direct talks involving "the whole spectrum of Afghan society".
The Afghan government was not part of the talks, but President Ashraf Ghani has said the government is willing to engage in peace talks with the Taliban under the right conditions, including a cease-fire. "Afghans have been bitten by this snake before", added his advisor Waheed Omer.More news: Nadal defies inspired Medvedev in five-set epic to win US Open