The raid in Quetta, the capital of strife-riven Balochistan province, was carried out late yesterday following an intelligence tip-off about the presence of fighters from the Lashkar-e-Jhangvi (LeJ) militant group.
"A team of anti-terrorist force (ATF) raided the compound and killed four militants after an exchange of gunfire," a senior local police official Abdullah Afridi told AFP.
Speaking off the record, a police official said the militants belonged to the LeJ - a faction of which claimed it had worked with the Islamic State group to carry out the Monday night raid that killed 61 people, the deadliest assault on a security installation in Pakistan's history.
The extent of any material support to local groups from IS remains unclear, but affiliation with the notoriously brutal outfit brings the promise of a far higher profile.
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The Balochistan government has also formed a joint investigation team (JIT) comprising officials from the army, police and intelligence agencies to probe Monday's attack.
Pakistan has been battling a homegrown Islamist insurgency since shortly after the US-led invasion of Afghanistan in 2001, though overall levels of violence have dropped following a series of militatry offensives in the country's western tribal regions.
The emergence of IS in Pakistan is seen as a major blow to the country's long-running efforts to quell the insurgency, and comes as the group's key rival Al Qaeda is losing strength in what was once its "home ground".