"We call on the leadership of the Taliban to welcome the wishes of Afghans for a long-lasting and real peace", he added.
Taliban sources said their leaders had also provisionally agreed a four-day truce during the annual Islamic feast of sacrifice, though supreme leader Sheikh Haibatullah Akhunzada still had to give his final approval. "Coinciding with the Independence Day of Afghanistan, the announcement has an even greater significance", Faisal said.
The fate of the hostages in Kunduz province - in an area that has recently fallen under Taliban control - was not immediately known and there was no statement from the insurgents.
By Sunday, the Taliban was expected to approve of the ceasefire, but leaders of the group said it might not be announced publicly.
At least 150 soldiers and 95 civilians were killed in a five-day siege, which eased last week when Afghan soldiers backed by US forces pushed back the heavily armed rebels.
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The June ceasefire - the first such truce in the country since the 2001 United States invasion - spurred hopes that a new path was opening for possible peace talks in the country to the end the almost 17-year-old war.
President Ashraf Ghani said it would come into effect on Monday if the Taliban accepted, but the militants have not responded yet. "It is time for peace".
Ghani did not mention any cease in fighting with the Islamic State group, which has expanded since it first emerged in the region in 2014 and was not included in the June ceasefire, or any of the other militant groups plaguing Afghanistan. "It is our hope, and that of the worldwide community, that the Afghan people may celebrate Eid al-Adha this year in peace, free from fear", he said.
The president's announcement was immediately welcomed in neighboring Pakistan, which has always been accused of fostering links with the Taliban's leadership and providing sanctuary to its fighters, and by North Atlantic Treaty Organisation secretary general Jens Stoltenberg.