The Taliban has not issued a statement to confirm or deny that Mullah Akhtar Mansour is dead, but Afghan officials said the US attack was successful.
The Pentagon said an airstrike in a remote area of the Afghanistan-Pakistan border region targeted Mullah Akhtar Mansour, but his death has not been confirmed.
The insurgents, who largely control the Afghan drug trade, are flush with cash and new recruits after the lucrative poppy harvest in Helmand province.
At least 28 people were killed and more than 300 injured when Taliban militants detonated a truck bomb and fought a gun battle near a government building during morning rush hour.
The release of the video comes just three days after the militant group declared the beginning of its fighting season — the time of year when the snow melts and Taliban fighters move to expand their territory.
'Jihad against the aggressive and usurping infidel army is a holy obligation upon our necks,' said a Taliban statement, as they announced the start of this year's fighting season.
Talks brokered by Afghanistan, Pakistan, China, and the US were expected to begin in early March, but the Taliban issued a statement saying it would not participate.
At least 20 people were reported killed and many more injured in separate suicide bombings in Kabul and the province of Kunar in eastern Afghanistan.
The Taliban said it seized armored personnel carriers and other equipment after Afghan forces withdrew from bases in the Musa Qala district of Helmand province.
The terror group crowned its encroachment in Afghanistan by broadcasting on an FM frequency to attract fresh recruits. Residents of Jalalabad said that the station remained quiet on Tuesday, suggesting that it had been destroyed.
The attack was the latest in a series to hit the Afghan capital this year as the Kabul government has pushed to revive a stalled peace process with the Taliban that broke down last year.
The latest in a long series of attacks by rogue policemen collaborating with insurgents took place at a checkpoint in the Chenartu district of Afghanistan's volatile southern province of Uruzgan.