A Nato spokesman would neither confirm nor deny the presence of foreign troops, but told the AFP news agency that the alliance had opened "a preliminary probe to determine if the allegations concerning civilian victims are credible".
The raid – which happened in the early hours of February 18th in the unsettled central Wardak Province – involved Afghan special forces and foreign soldiers, according to the charity involved, the Swedish Committee for Afghanistan (SCA).
Officials from the United Nation's UNAMA mission also pointed the finger at Afghan forces, condemning the raid during which it said two patients and a 15-year-old boy were summarily executed without explanation.
The Swedish charity, which runs health, education and other development programmes in almost half of Afghanistan's 34 provinces, called on Thursday for "explanations" from the Afghan government and foreign forces, as well as an independent investigation.
In Stockholm, Sweden's minister for international development cooperation, Isabella Lövin, condemned recent attacks against clinics in Syria, Yemen and Afghanistan, which she said were "deeply worrying".
"The countries concerned have a duty to investigate crimes against international law, including in the case" of the Wardak attack, she added in a statement, recalling that Afghanistan was one of the biggest recipients of Swedish development aid.
Sweden is not a member of Nato, but contributes around 50 troops to assist and advice Afghan security forces as part of the international mission in Afghanistan. The Swedish Afghanistan Committee is a non-affiliated development aid charity operating in the region.
On paper Nato's remaining 13,000 soldiers in Afghanistan are only there for training and as advisers for the Afghan army.
But in practice they are increasingly finding themselves drawn into fighting. Three were injured in a class with Taliban fighters at the start of this week.
The Afghan Taliban on Thursday released a video which they said showed anger trigged by the raid in Tangi Saidan.
"It's a barbaric attack!" says one old man, presented as a local resident. "Afghan civilians were killed in this attack," he added in the 13-minute video. Three bodies were then shown, described as "martyrs of the hospital".
While far less active online than the militant Isis group, Afghan Taliban often film propaganda videos allegedly showing the "barbarity" carried out by foreign fighters in their country.
The day after the attack, Afghan authorities gave conflicting accounts of what happened. The governor of Wardak province, Hayatullah Hayat, said the zone was under Taliban control and talked about an "operation against insurgents" that night, while denying that it involved the clinic.
Wardak, south-west of the capital Kabul, has been the scene of some of the most violent battles between Nato forces and the Taliban.