Pakistan rejected the claim as false and misleading, saying it "precisely targeted military installations and terrorist support infrastructure", on Monday night.
Hamdullah Fitrat, the deputy spokesman for the Taliban, said the airstrike took place at 9pm and targeted the Omid 2000-bed drug rehabilitation hospital.
"Large parts of the hospital have been destroyed, and there are fears of heavy casualties," he said in a post on X.
"Sadly, the number of those killed has so far reached 400, with up to 250 others injured."
Rescue teams were at the scene working to control the fire and recover the victims, he said.
Reuters could not verify the casualty numbers and the Pakistani military could not be reached for comment outside business hours.
The Pakistani Information and Broadcasting Ministry said the Afghan Taliban claim was "misreporting of facts".
In an overnight post on X, it said that Pakistan targeted military installations and "terrorist support infrastructure" including technical equipment storage and ammunition storage of the Afghan Taliban and Pakistani Taliban militants in Kabul and Nangarhar that were being used against Pakistani civilians.
"Pakistan's targeting is precise and carefully undertaken to ensure no collateral damage is inflicted," the post said.
"This misreporting of facts as drug rehabilitation facility seeks to stir sentiments, covering illegitimate support to cross-border terrorism."
The International Human Rights Foundation condemned the attack and called for an independent international investigation into the incident, saying it was "deeply disturbed by reports that many of the victims were unarmed civilians undergoing treatment".
Fierce fighting between the South Asian neighbours erupted last month with Pakistani airstrikes in Afghanistan that Islamabad said targeted militant strongholds.
Afghanistan called the strikes a violation of its sovereignty that targeted civilians and launched its own attacks.
Both sides claim to have inflicted heavy damage on the other but independent verification has not been possible.
Islamabad says Kabul provides a safe haven to militants launching attacks on Pakistan. The Taliban deny the allegation, saying tackling militancy is Pakistan's internal problem.
The conflict had ebbed amid attempts by friendly countries, including China, to mediate and end the fighting before flaring up again.
Richard Bennett, the UN Special Rapporteur for human rights in Afghanistan, said he was "dismayed" by fresh reports of Pakistani airstrikes and civilian deaths.
"My condolences. I urge parties to de-escalate, exercise maximum restraint and respect international law, including the protection of civilians and civilian objects such as hospitals," he said in a post on X.
