Algeria sent a letter to FIFA’s refereeing commission, with particular reference to the first-half incident when Argentina’s Messi stood on the calf of Algeria captain Aissa Mandi.

Algeria supporters screamed for Messi to be sent off as he caught Mandi from behind flush on the calf with a raised boot, but the forward was not punished and went on to score a hat-trick, sealing the result.

Algeria also alleges an elbow from Argentina midfielder Mac Allister in the face of Ibrahim Maza in the second half of the Group J clash in Kansas City went unpunished by Poland’s Szymon Marciniak.

The experienced referee, who was in charge of the 2022 FIFA World Cup final in Qatar in which Argentina beat France on penalties, was within a metre of the incident when Mac Allister appeared to body-check Maza with a raised elbow.

Algeria’s complaint raises questions about Marciniak’s performance and that of his video assistant referees (VAR), led by compatriot Tomasz Kwiatkowski.

The Messi incident caused a social media storm with fans debating whether his star status played any part in a lack of punishment.

It was also referenced by South Africa coach Hugo Broos when he was asked to react to his midfielder Themba Zwane having his ban at the tournament extended to three matches after a red card in the opening game against Mexico.

“When I see what happened with Messi, I don't agree, certainly not, with what happened to my player. When you see the situation, the Mexican player blocked my player, and Themba tried to get over him, and he put his arm over his shoulder. That's all he does,” Broos said.

“And you get a red card for that and then a three-game suspension? Sorry, but this is much, much, much too severe.

"I don't want that Messi gets a red card, because a player of that quality has to be on the pitch as you saw [against Algeria], but what was the difference between that and Zwane?”

Argentina faces Austria in Dallas on Tuesday (AEST) while Algeria will meet Jordan in San Francisco.