Among the index-heavy winners in Stockholm are engineering giant Sandvik, up 6.3 percent, and mining group Boliden, up 6.2 percent. But the rise was broad.
The turnaround came after US President Donald Trump said he sees a quick end to the war with Iran. Stock markets in London, Paris and Frankfurt also rose.
The price of oil fell and closed just below $90 per barrel after trading above $119 overnight Monday.
But reports of a tanker explosion in the Persian Gulf and of a refinery in the United Arab Emirates being closed due to a fire caused oil prices to rise for a few hours in the afternoon.
And the uncertainty over when the US and Israel's war against Iran might end remains. Shortly after Tuesday night's statement that the war could soon be over, Trump said that the attacks will continue "until the enemy is totally and decisively defeated."
The OMXS index, down 1.7 percent on Monday, has risen 2.3 percent since the turn of the year.
