Afghan President Ashraf Ghani announced Saturday an extension of the government's week-long ceasefire with the Taliban, as both sides observed a halt in hostilities for Eid.

In a rare televised address to the nation, Ghani also asked the Taliban to extend their three-day ceasefire which is due to end Sunday.

"I order the security forces to remain on their defensive positions," Ghani said, adding details of the extension would be released later.

The government's ceasefire was due to end Tuesday.

His announcement comes as Taliban fighters and Afghan security forces hugged and took selfies with each other across the country as an unprecedented ceasefire in the war-torn country held for the second day of Eid.

Carrying assault weapons and rocket-propelled grenade launchers, members of Afghanistan's biggest militant group travelled by car and motorbike through the contested district of Bati Kot in eastern Nangarhar province, waving Afghan and Taliban flags.

Afghan forces manning checkpoints offered Eid greetings to the Taliban, embracing and posing for photos with the same people they are usually trying to kill -- a scene that would have been unthinkable only a few days ago.

Villagers also flocked around the insurgents, hugging them and happily taking selfies with the heavily armed fighters as they celebrated the Muslim holiday capping the holy month of Ramadan.

"I am here to offer greetings to our brothers in the police and army," Taliban commander Baba told AFP.

"We have held the ceasefire well so far. Everyone is tired of war and if our leaders order us to continue the ceasefire, we will hold it forever."

A Taliban fighter on a motorbike carrying the Afghan and Taliban flags welcomed the ceasefire, but said long-lasting peace would only be achieved if US forces left the country.

"We want an Islamic country and government. This cannot happen unless America leaves (Afghanistan)," he told AFP.

The Taliban announced a ceasefire for the first three days of Eid, which started Friday, promising not to attack Afghan security forces for the first time since the 2001 US invasion.

They said they would continue attacking US-led NATO troops.

That came after Ghani announced that police and troops would cease operations against the Taliban for eight days, starting last Tuesday -- though he warned that operations against other militants, including the Islamic State group, would continue.

Afghan Deputy Interior Minister Masood Azizi told AFP both sides had so far respected the ceasefire.

"Luckily it's going well so far," Azizi said.

Bati Kot is on the highway connecting the Nangarhar provincial capital of Jalalabad with Torkham, one of the major border crossings into Pakistan, which has long been accused of supporting the Taliban and providing safe haven to its leaders, charges it denies.

Afghans shared photos on social media purportedly showing Taliban fighters around the country gathering with security forces and locals for the holiday.

The bizarre images served as powerful propaganda for both sides and have fanned hopes among war-weary Afghans for the ceasefire to continue.

"Look, they are brothers. If their leaders come, sit and talk just like their soldiers we will have peace tomorrow," Said Hasibullah posted on Facebook under a photo purportedly showing a Taliban fighter and Afghan soldier having a cup of tea together.

The Taliban had "exploited" the opportunity to show their popularity among ordinary Afghans, a Western diplomat in Kabul told AFP.

"(That's) no bad thing if they are able to see the benefits of talking not fighting," he said.

The unusual bonhomie between the two sides came as Ghani confirmed that Pakistani Taliban chief Maulana Fazlullah had been killed in a US drone strike.

US forces targeted Fazlullah in a counterterrorism strike on Thursday in eastern Kunar province, close to the border between Afghanistan and Pakistan, US officials said, without confirming his death.

Ghani said Pakistani leaders had assured him the strike was a "great step toward building trust between the two nations," while urging them to "bring (the) Afghan Taliban residing in Pakistan to the negotiation table."

On Tuesday, Pakistan's powerful army chief General Qamar Javed Bajwa visited Kabul where he met with Ghani.