US ski magazine Mountain Gazette reported that one of the dead was American professional skier Kyle Smaine.
Two men who were travelling with Smaine posted Instagram updates saying he had been killed in the avalanche.
Austria's foreign ministry said an Austrian national had also died in the "tragic incident" but declined to give further details.
A local police spokesman said only that emergency rescue teams had "confirmed the death of the two men" and that their identities or nationalities would be released after thorough ID checks.
The two men had been outside the patrolled areas of a ski resort in Otari village along with several other skiers and snowboarders when the avalanche took place on Sunday.
The others were able to return down the mountain.
According to Mountain Gazette, Smaine, 31, had been with fellow professional skier Adam U and the publication's senior photographer Grant Gunderson when he was killed.
"Yesterday was my absolute worst nightmare scenario," Gunderson wrote in an Instagram post published Monday.
He said an avalanche had been triggered by a skier, and Smaine "was thrown 50 metres by the air blast and buried and killed".
Last week, a cold snap blanketed much of Japan in heavy snow, including Nagano, which draws many overseas tourists during ski season.
An avalanche warning and snow warning are currently in place for the area.
Fans were quick to leave tributes to Smaine on a video he posted to Instagram on Sunday showing him skiing off-piste.
"This is what brings me back to Japan each winter. Unbelievable snow quality, non-stop storms, and really fun terrain that seems to get better (the) more exploring you do," he wrote in a comment accompanying the video.
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