Jarstein walked out of a post-match interview with Norway's TV2 on Tuesday, throwing a headset in anger, after the reporter asked him if he was at fault for Slovenia's goal in Norway's 2-1 win.
Jarstein apparently had not cooled down by Wednesday, when he reportedly threatened to punch a photographer taking his picture as he left the Oslo hotel where the national team was staying.
The goalkeeper apologized for both incidents in a statement posted on the Norwegian Football Association's website.
"I didn't want to be interviewed or have my picture taken and I expressed that clearly," he said of the incident Wednesday. "When I was photographed anyway I felt strongly provoked and made that clear. I regret that my comments were perceived as a real threat, and I strongly apologize for my behaviour."
He also expressed regret for abandoning the TV interview but said "I felt the focus of the interview was wrong."
Slovenia took the lead after scoring from a rebound when Jarstein failed to hold on to a free kick in the first half of Tuesday's match. An injury-time penalty by John Arne Riise secured the win for Norway.
The Norwegian FA's information chief, Svein Graff, welcomed Jarstein's apology.
"We both agree that his reaction yesterday and today was unacceptable," Graff said. "It is very important that he has realized that this was inappropriate behaviour and silly."