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Gylfi Sigurdsson almost put Iceland in front early on but his angled shot and follow-up were both saved.
Nani slotted in for Portugal but Iceland worked a shock equaliser when Birkir Bjarnason volleyed home.
Cristiano Ronaldo had a header saved for an unconvincing Portugal, while Iceland went close late on when Alfred Finnbogason had a shot saved.
Ronaldo came into the tournament fresh from scoring the winning penalty for Real Madrid in their Champions League final shootout victory over Atletico Madrid as he added another club trophy to a long list.
Honours on the international stage have eluded him, however, and unless the forward can replicate his club scoring achievements for his country that is likely to continue.
Ronaldo, who won his 127th cap and equalled the Portuguese record set by Luis Figo, showed a glimpse of his quick feet to get in a precise cross for Nani, whose six-yard header was saved.
But he could only kick fresh air from 10 yards out as he failed to make contact with a long Pepe pass, then sent a 20-yard half-volley wide and had his late header saved as he endured a frustrating evening in Saint-Etienne.
Iceland are the smallest nation ever to reach a European Championship finals, with a population of approximately 330,000, and have no professional clubs.
However, they beat the Netherlands twice on the way to qualifying for the tournament in France and added another chapter to their fairytale on their major tournament debut.
Goalkeeper Hannes Thor Halldorsson had more touches than any other Iceland player in the first half (30) but his side kept Portugal within reach.
Their efforts paid off when Bjarnason caught right-back Vieirinha out of position to score from Johann Gudmundsson's cross to the far post.
And, despite Iceland having just 27.7% of possession overall, they gave Portugal a couple of further scares before the final whistle.
"Honesty, endeavour - that's what Iceland are all about," said BBC Radio 5 live pundit and former England international Chris Waddle.
"They were getting a football lesson in the first half but they never threw in the towel. They've got their rewards, and their fans are going absolutely wild."
On the basis of this game, the answer would have to be yes.
The move for the first goal did not involve Ronaldo and came courtesy of quick passing down the right before Andre Gomes put in a low cross for Nani to finish.
However, with Ronaldo having a quiet night by his standards, no other Portugal player stepped up to make the difference.
They also conceded an equaliser that suggests vulnerabilities in defence they will have to resolve if they want to win a major tournament for the first time.
Portugal boss Fernando Santos: "We should've scored more goals: that's no secret. There's always difficulties in the first game. I think we'll bounce back to play two great matches."
Iceland joint manager Heimir Hallgrimsson: "It's down to teamwork. You can't put one player to stop a guy like Ronaldo. It has to be a team effort, closing the areas.
"There were a lot of players responsible for Ronaldo tonight. We did a really good job - well done the lads."
Iceland play group leaders Hungary in Marseille at 17:00 BST on Saturday, 18 June, while Portugal play Austria at 20:00 BST on the same day in Paris.
Match ends, Portugal 1, Iceland 1.
Second Half ends, Portugal 1, Iceland 1.
Attempt blocked. Cristiano Ronaldo (Portugal) right footed shot from outside the box is blocked.
Alfred Finnbogason (Iceland) is shown the yellow card for hand ball.
Hand ball by Alfred Finnbogason (Iceland).
Attempt blocked. Cristiano Ronaldo (Portugal) right footed shot from outside the box is blocked.
Nani (Portugal) wins a free kick in the attacking half.
Foul by Teddy Bjarnason (Iceland).
Ricardo Quaresma (Portugal) wins a free kick on the right wing.
Birkir Bjarnason (Iceland).
Substitution, Iceland. Teddy Bjarnason replaces Johann Berg Gudmundsson.
Foul by Cristiano Ronaldo (Portugal).
Hannes Thór Halldórsson (Iceland) wins a free kick in the defensive half.
Corner,  Portugal. Conceded by Kári Arnason.
Offside, Portugal. Raphael Guerreiro tries a through ball, but Cristiano Ronaldo is caught offside.
Attempt missed. Ricardo Quaresma (Portugal) right footed shot from outside the box is high and wide to the right. Assisted by Raphael Guerreiro.
Attempt saved. Alfred Finnbogason (Iceland) left footed shot from the centre of the box is saved in the centre of the goal. Assisted by Gylfi Sigurdsson.
Attempt saved. Cristiano Ronaldo (Portugal) header from the centre of the box is saved in the centre of the goal. Assisted by Nani with a cross.
Substitution, Portugal. Eder replaces André Gomes.
Pepe (Portugal) wins a free kick in the defensive half.
Foul by Alfred Finnbogason (Iceland).
Attempt missed. Pepe (Portugal) header from the left side of the six yard box is just a bit too high. Assisted by Ricardo Quaresma with a cross following a corner.
Corner,  Portugal. Conceded by Aron Gunnarsson.
Attempt blocked. Cristiano Ronaldo (Portugal) right footed shot from outside the box is blocked.
Cristiano Ronaldo (Portugal) wins a free kick in the attacking half.
Foul by Aron Gunnarsson (Iceland).
Substitution, Iceland. Alfred Finnbogason replaces Kolbeinn Sigthorsson.
Offside, Portugal. Renato Sanches tries a through ball, but Cristiano Ronaldo is caught offside.
Corner,  Portugal. Conceded by Ari Freyr Skúlason.
Corner,  Portugal. Conceded by Hannes Thór Halldórsson.
Attempt saved. Ricardo Quaresma (Portugal) right footed shot from the right side of the box is saved in the bottom right corner. Assisted by André Gomes.
Substitution, Portugal. Ricardo Quaresma replaces João Mário.
Attempt blocked. João Mário (Portugal) right footed shot from outside the box is blocked. Assisted by Renato Sanches.
Dangerous play by Renato Sanches (Portugal).
Aron Gunnarsson (Iceland) wins a free kick in the defensive half.
Attempt missed. Cristiano Ronaldo (Portugal) right footed shot from outside the box is too high. Assisted by Nani.
Foul by André Gomes (Portugal).
Gylfi Sigurdsson (Iceland) wins a free kick in the defensive half.
Attempt missed. Nani (Portugal) header from the centre of the box is close, but misses to the left. Assisted by Raphael Guerreiro with a cross following a set piece situation.
Substitution, Portugal. Renato Sanches replaces João Moutinho.
Iceland earned a memorable point on their European Championship debut, holding Portugal to a draw in Group F.