The Taliban shot dead the head of the Afghan government's media information centre on Friday near a mosque in the capital, days after warning they would target senior administration figures in retaliation for increased air strikes.

The assassination of one of the government's leading voices follows another bloody day of fighting in Afghanistan as the war spills into Kabul for the first time in months.

It also comes hours before the UN Security Council meets in New York to discuss the conflict.

"Unfortunately, the savage terrorists have committed a cowardly act once again and martyred a patriotic Afghan,” interior ministry spokesman Mirwais Stanikzai said of the death of Dawa Khan Menapal.

Menapal was popular in Kabul's tight-knit media community, and known for pillorying the Taliban on social media — even jokingly at times.

Former presidential spokesman Sediq Sediqqi said he was "utterly shocked and devastated".

"We lost another great soul,” he said.

The Taliban claimed responsibility for Menapal's death, with spokesman Zabihullah Mujahid sending a message to the media saying "he was killed in a special attack carried out by mujahideen".

The murder comes after the militants warned on Wednesday of more attacks targeting Afghan government leaders, a day after Defence Minister Bismillah Mohammadi escaped an assassination attempt in a bomb-and-gun attack.

The Afghan and US militaries have stepped up air strikes against the insurgents in a string of cities, and the Taliban said Tuesday's Kabul raid was their response.

Fighting in Afghanistan's long-running conflict has intensified since May, when foreign forces began the final stage of a withdrawal due to be completed later this month.

The Taliban already control large portions of the countryside, and are now challenging government forces in several provincial capitals.

Government forces continue to hit Taliban positions with air strikes and commando raids, and the defence ministry boasted on Friday of eliminating more than 400 insurgents in the past 24 hours.

Both sides frequently exaggerate battlefield casualty figures, making independent verification virtually impossible.

But even as Afghan officials claimed to be hitting the Taliban hard, security forces have yet to flush out the militants from provincial capitals they have already entered — with hundreds of thousands of civilians forced to flee in recent weeks.

In the western city of Herat, a steady stream of people were leaving their homes in anticipation of a government assault on positions held by the Taliban.

"We completely evacuated,” said Ahmad Zia, who lived in the western part of the city.

"We have nothing left and we do not know where to go,” he told AFP.