The militants stormed the northern provincial capital on Monday, effectively overrunning it in their biggest triumph since being ousted from national power in 2001.
Afghan troops backed by US air support launched a counter-offensive on Tuesday to retake the city, but the Taliban video suggested they could be looking to hold onto their gains. Some analysts had speculated they might melt away after scoring a symbolic victory.
The 10-minute clip posted on Facebook opens with a shot of Kunduz main square where Taliban cadres cheer as they raise their white flag under the wary gaze of subdued-looking residents.
Elsewhere fighters show off tanks and armoured cars they have captured, chanting "Allahu Akbar" (God is the greatest) and roaming the streets in seized pick-up trucks.
A militant tells a crowd that they will bring Islamic sharia law, as they reply "Inshallah" (God willing).
The video ends with a message from the Taliban's newly appointed leader Mullah Akhtar Mansoor, though he does not appear on screen.
The message declares: "We do not believe in revenge" and announces a "general amnesty" for government troops wishing to defect.
Mansour's message also instructs government officials and doctors in Kunduz to carry on work as normal, and tells residents the Taliban will ensure their safety and protect their property.
"Kabul should accept this bitter reality of our victory and it should worry about rest of the state," it concludes.
Analysts say that whether or not the Taliban remain in the city, the Kunduz assault will boost Mansoor's image within insurgent ranks as he seeks to cement his authority by burnishing his credentials as a commander.
The relative ease with which the militants took the city on their third attempt — in less than a day and seemingly without major losses — also bodes badly for the Afghan National Army, which has been fighting the Taliban without Nato combat troops since the start of the year.
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