Iceland was 2-0 up with five minutes left at the Roudourou stadium in Brittany and looked set to hand France its first loss since winning the World Cup in July.
Nigeria will face Argentina in its final group match on Tuesday in St. Petersburg and African nation wins, it will advance to the round of 16.
Iceland's opening game of the tournament saw them hold Argentina to a 1-1 draw to give Heimar Hallgrimsson's side a fighting chance of reaching the last 16.
Halldorsson said it was a dream come true to face the "best player in the world", adding his side had earned an important point in its first-ever World Cup match.
Messi denied that the draw would affect the team in its next Group D contest on Thursday against Croatia.
The small Nordic island nation's team created several first-half chances despite having only 22 per cent possession and pushed back Argentina's waves of second-half attacks.
Argentina last won the World Cup in 1986 when the legendary Diego Maradona single-handedly carried them to the title.
Spain beat Portugal at the 2010 World Cup, and again in the semifinals of the 2012 European Championship, going on to win the tournament both times.
Argentina is among the shortest teams at the tournament at 1.79 meters, coach Jorge Sampaoli has put special emphasis on height during tactical work at the team's training center in the Moscow.
The Icelandic fairytale is made more charming by its vociferous and passionate fans, who made the "thunderclap" war chant the soundtrack of that summer in Euro Cup 2016.
Argentina, Iceland, Croatia and Nigeria are part of Group D of the World Cup.
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