NASHVILLE, Tenn. — Tennessee’s state medical examiner said Tuesday that investigators have been hesitant to conclude that Steve McNair’s girlfriend killed the NFL star and herself because she didn’t appear to have a motive, but that murder-suicide is the most likely scenario.

After the couple was discovered shot to death on Saturday, police were quick to label McNair’s death a homicide. He had been shot twice in the head and twice in the chest, while 20-year-old Sahel Kazemi was dead from a single gunshot to the head. Under her body was a gun she had purchased less than two days before the killings.

Investigators were waiting on ballistics tests on the weapon before issuing a ruling on Kazemi’s death, which medical examiner Bruce Levy said could come in the next few days. Kazemi’s gun purchase, which was revealed on Monday, is a strong indication that she was responsible, he said.

‘‘If we had known on Sunday about the gun I think we would have been very comfortable in ruling murder-suicide,’’ he said. ‘‘I’ll be very surprised now if they rule it isn’t.’’

Levy said an apparent lack of motive by Kazemi has made investigators careful about exploring every possibility, including the unlikely scenario that a third party could have staged the scene. Their relationship lacked typical indicators of trouble — such as concerned family members or police reports and protection orders.

‘‘The thing we always hear is, ’We should have seen this coming,’’’ he said.