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Afghan forces resumed their offensive against the Taliban on Saturday, as the government ended a unilateral ceasefire against the insurgents.

President Ashraf Ghani declared an end to the government's unilateral ceasefire with the Taliban, which lasted 18 days.

Ghani had extended it once and overlapped with the Taliban's unilateral three-day truce for Eid.

He said it had been "98 percent successful" but the truce was now at an end.

"The ceasefire is over. The Afghan security and defence forces are allowed to restart their military operations," Ghani told reporters.

During the three day ceasefire there were no reports of fighting in the country, which has witnessed war for the past 17 years.

Unprecedented scenes were witnessed as Taliban fighters and security forces spontaneously hugging and taking selfies to celebrate the Eid holiday, which ends the holy month of Ramadan.

The militants were also mobbed by relieved civilians, who have borne the brunt of the war, raising fresh hopes of a new push for peace talks. 

The Taliban's leaders appeared to have been alarmed by the scenes, and ordered their men back to their posts on Sunday.

This week, a small peace rally was bombed by militants, killing at least eight people.

Ghani said he was open to a new ceasefire with the militants.

"[It's the] Taliban's turn to give a positive response," he said.

"I am ready to extend the ceasefire anytime when the Taliban are ready," he said at a press conference. 

The Taliban vowed Tuesday to continue the battle against the government and NATO, brushing aside rising civilian casualties.

The insurgents returned to the battlefield last week after refusing a government request to extend their ceasefire, launching attacks across the country that have seen scores killed or injured.

The truces did not extend to the Islamic State group, which has a relatively small but potent presence in Afghanistan, and launched two deadly attacks on ceasefire revellers during Eid.