Sigurdsson returned to the national team during a Euro 2024 qualifier against Luxembourg last Friday. After impressing in his 22-minute cameo, he was handed a full start for Monday night's fixture against Liechtenstein.
He took just 22 minutes to find the opener from the spot, which sent the home crowd into raptures at the Laugardalsvollur Stadium in Reykjavik.
The former Everton player scored another after half-time, which helped Iceland seal a comprehensive 4-0 victory against Liechtenstein. Sigurdsson was cheered every time he touched the ball, which made it a special occasion for the 34-year-old.
"It was hard not to hear, it was already in my warm-up and when I came in. I have never received such a reception here, it was an extra wild welcome,' he told Fotbolti.
Sigurdsson earned his international call-up after he joined Lyngby in the Danish league to revive his career. However, he believes that there is still scope for improvement and will need "a few months more" to fire on all cylinders.
"I think. In Lyngby, I may have trained fully 10-14 times. It has gone quickly. I know there is a long way to go and it will probably be a few months before I am in top form," he added.
He made his debut in the Superliga on September 22, after staying away from professional football for 853 days.