The command said in a press release EUFOR soldiers were fired at when they arrived at the location where the arrest was to be carried out.
The soldiers shot in self-defence and two persons who were in the house which was fired at were wounded, the press release said, adding that Abazovic wounded himself. No EUFOR member was hurt.
EUFOR recalled that the operation was carried out on an order of the Cantonal Court in Sarajevo, and said the case was now in the jurisdiction of the State Prosecutor's Office.
Hospital sources in Foca confirmed that Abazovic was wounded, as were his 11-year-old son Dragoljub and wife Rada, who succumbed to the wounds during the day. Abazovic and his son underwent surgery and are out of danger.
The Bosnian Serb entity police did not take part in the operation, said spokesman Radovan Pejic.
Entity President Dragan Cavic sent a protest letter to EUFOR commander Gianmarco Charini, demanding an investigation into who was responsible in the Rogatica operation.
Cavic labelled the operation a "manifestation of brute force and a violation of the European Convention on Human Rights," and underlined that Abazovic should have been arrested by Bosnia's entity and state security agencies because his name was on a public indictment.
Cavic added the death of Abazovic's wife and wounding of his underage son undermined EUFOR's reputation and confidence in its troops.