He said the government had announced the ceasefire with the Taliban only and Afghan forces should be careful about activities of other militant groups.
A provincial council member, Sayyed Asadullah Sadat said the clashes started early morning after Taliban launched coordinated attacks on security checkpoints in Aaq Tipa locality of Qala-e-Zal district, the provincial capital of Kunduz.
"This ceasefire is an opportunity for the Taliban to realize that their violent campaign is not winning them hearts and minds but further alienating the Afghan people from their cause", Ghani said. "I also hope other terrorist groups such as Daesh don't disrupt it". "They will kill more to make up for their ceasefire days".
"We have been stopping fighting during the Eid days, but we would not announce it publicly due to security reasons", Mujahid said.
"That the Taliban chose their "unilateral" cease-fire to coincide with the Afghan government's announcement is a cautious step toward public cooperation with the government on peace", said Ahmad Shuja, an Afghan analyst and editor-in-chief of the Georgetown Public Policy Review.
In first, Afghan Taliban announce cease-fire for Eid holiday
He said there was a report of a single Taliban casualty but the group has not commented.
Ghani endorsed a recommendation by the clerics for a cease-fire with the Taliban.
"We hope this ceasefire continues", he said in an interview with Tolo News.
The decision to suspend fighting for the first three days of Eid, the holiday that marks the end of the fasting month of Ramadan and a time when Muslims visit family and friends, took many in the war-weary country by surprise.
The move was greeted with optimism from NATO, with General Curtis Scaparrotti, NATO's supreme commander in Europe, giving an upbeat assessment this week of the struggle against the Taliban.
The attack began at 9.50 am when a suicide bomber detonated explosives outside the Education Department office in Jalalabad.
Taliban rebels stormed an Afghan National Army (ANA) base in Kandahar's Shah Walikot district, local media quoted a regional military spokesman as confirming.
No survivors after small plane crashes in Kenya
The CS208 plane, registration number 5Y-CAC, was flying from a Kitale airstrip in Trans-Nzoia County to Jomo Kenyatta International Airport when it lost contact with control tower at 5pm.