The trading day started off sharply lower, but at lunchtime US President Donald Trump announced that "very good and productive" talks had been held with Iran on a solution to the conflict.
The OMXS index was up a little over 2 percent at one point, but then fell back by the end of the day.
On the OMXS30 index, which has the most-traded shares, most companies rose. Mining group Boliden and truck manufacturer AB Volvo fared best, rising 3.9 and 3.2 percent respectively.
At the other end of the spectrum was telecom operator Telia, which fell 1.7 percent.
The price of oil fell back, and a barrel of North Sea oil (Brent) was trading just under $100 at 5:30 p.m.
The price of gold was trading late in the afternoon at just over $4,350 per ounce, up from around $4,200 earlier in the day.
The leading European stock exchanges moved in different directions during the day. Frankfurt and Paris rose, while London was marginally down. In New York, markets opened sharply higher before falling back somewhat after a few hours of trading.
