According to sources, the clashes occurred in eastern Afghanistan's Nangarhar Province, in areas bordering Pakistan, Xinhua reported.
Sources said that heavy weapons were used by both sides and that there were casualties. The Afghan and Pakistani governments have not yet issued any statement on the latest clashes.
Earlier, Zabihullah Mujahid, spokesperson for the Afghan government, said that Afghanistan would respond to airstrikes carried out by Pakistan on Sunday.
The Afghan side said that the Pakistani military on Sunday carried out airstrikes on the bilateral border areas, killing 18 people and injuring five others.
Pakistan said Sunday that it had carried out intelligence-based, targeted strikes on seven militant camps and hideouts in the Pakistan-Afghanistan border area, following a series of suicide bombings, and killed over 80 terrorists.