KABUL, June 13 (Xinhua) -- Fighting between government forces and Taliban militants is still going on in parts of Afghanistan as the government's ceasefire came into effect on Tuesday.

The militant group, besides engaging the security forces in parts of the country, also conducted a deadly car bomb in Muqar district of the eastern Ghazni province on Tuesday, killing five police and injuring several others.

The Afghan government, in an effort to encourage Taliban group to join peace process and boost national reconciliation, announced a seven-day ceasefire starting Tuesday.

However, Taliban outfit, for the first time, declared a three-day truce which comes into effect from the first day of Eidul Fitr, the second largest annual religious festival probably falling on Thursday or Friday depending on sighting the moon.

Taliban militants obviously have overlooked the government unilateral ceasefire and stormed security checkpoints in Khwaja Sabz Posh district, Faryab province on Tuesday night, killing two police and injuring four others, police spokesman in the northern region Sayyed Sarwar Hussaini said Wednesday.

Six Taliban fighters were also killed in the fight, according to Hussaini.

Moreover, a bomb blast carried out by the militants in Jalalabad city, the capital of the eastern Nangarhar province, claimed the life of a 10-year-old child and injured seven others on Wednesday.

The Afghan government in its ceasefire has excluded al-Qaida and the hardliner IS, saying the security forces would continue to chase the said groups' insurgents elsewhere in the war-battered country.

Similarly, Taliban outfit has also announced that its three-day truce would not cover the U.S.-led coalition forces and its militants would continue to attack the foreign forces stationed in Afghanistan.

However, the people of Afghanistan have welcomed the ceasefire announced by both the government and Taliban outfit, hoping the truce could lead to permanent ceasefire and lasting peace in their country.