Afghanistan's Ministry of Defence said its forces killed 28 fighters in the eastern province of Nuristan who had crossed the border from Pakistan.
In a statement posted to X, the Taliban's defence ministry said it had engaged in clashes with the opposing group on Sunday.
The ministry alleged that most of the fighters were former Afghan government security personnel recruited by Pakistan's intelligence services with promises of asylum and well-paid employment in foreign countries. It also claimed the fighters included ISIL members supported by Pakistani militias.
Pakistan's Ministry of Information and Broadcasting rejected the allegations, describing them in a post on X as "frivolous, baseless and devoid of any truth."
Pakistan denied that its security forces or intelligence agencies were involved in the clashes in Nuristan, or that they had recruited or trained former Afghan security personnel, or facilitated ISIL or other armed groups in Afghanistan.
Pakistan's information ministry also said the Taliban "should take credible and verifiable action against terrorist organisations operating from its territory" and fulfil its obligation so that "Afghan soil will not be used for terrorism against Pakistan or any other country rather than attempting to deflect responsibility through fabricated accusations."
The incident follows a period of sharply escalating tensions between the two countries.
Last week, Pakistan launched air strikes on 10 locations in Afghanistan it said were used to store and launch drones, some of which had been used in cross-border attacks. A spokesman for the Afghan Taliban government said those strikes, carried out on Thursday, killed at least four people, and promised an "appropriate response."
Sunday's clashes also follow Pakistani air strikes on September 21 that Islamabad said killed 28 fighters. Afghan officials said civilians were killed in those strikes. The United Nations mission in Afghanistan confirmed three civilian deaths.
Pakistan has repeatedly accused Afghanistan of sheltering fighters who carry out attacks on its territory, a charge Kabul denies.
