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Afghan President Ashraf Ghani rejected on Sunday the resignations of the intelligence chief, the interior and defence ministers, as the government faces fierce criticism over an increasingly deadly insurgency raging in the country.

Ghani called on Defence Minister Tariq Shah Bahrami, Interior Minister Wais Ahmad Barmak and intelligence chief Masoom Stanekzai to continue their duties, after rejecting their resignation letters submitted Saturday and demanding they help bolster the country's defences.  

"President Ghani did not approve their resignations... and gave them the necessary instructions to improve the security situation," said a palace statement.

Earlier, Saturday Ghani's powerful national security adviser Mohammed Haneef Atmar had resigned, in a blow to the embattled unity government before parliamentary elections scheduled for October.

The Ghani administration has been widely criticised for its inability to counter the energised insurgency. The Taliban have intensified assaults on police and troops across the country and the Islamic State group has targeted the capital Kabul.

The resignations come amid a violent series of incidents, as the insurgent group Taliban have expanded their footprint across Afghanistan, launching a relentless assault on Ghazni, a strategic city near Kabul earlier this month.

Militants held large parts of the city for days and Afghan forces needed US air power to push them back, resulting in widespread destruction and estimates of hundreds of deaths.

The resignation letters came a week after Ghani offered a conditional three-month ceasefire to the Taliban, a move welcomed by the US and NATO after nearly 17 years of war.

The Taliban have yet to officially respond to the offer. A brief ceasefire in June had sparked hopes that a path for talks with the insurgents was opening.