The Barcelona superstar left the field in tears after missing a spot-kick in the Copa America Centenario final shootout against Chile on Sunday.
He promptly told reporters he was quitting, throwing Argentine football into turmoil ahead of the 2018 World Cup in Russia.
“He has to stay because he still has playing days ahead of him,” Maradona was quoted as saying by La Nacion newspaper online.
“He will go to Russia in form to be world champion.”
Messi, 29, is widely rated as the best player in the world, but Sunday’s loss was his fourth defeat in an international final for Argentina.
After an outpouring of disappointment by fans online, Macri joined the calls for the Barcelona superstar to stay with Argentina.
“He called him and told him how proud he feels of the national team’s performance and asked him not to listen to the criticism,” a spokesman for Macri told AFP by telephone.
Argentine football ‘disaster’
The 1986 World Cup winner Maradona, 55, blamed Argentina’s recent lack of trophies on the country’s football association (AFA).
He accused it of not supporting Messi and letting him take the blame for Sunday’s defeat.
“Those who are saying he should quit are doing it so that we won’t see what a disaster Argentine football has become,” La Nacion quoted Maradona as saying.
Messi and the squad landed back in Buenos Aires on Monday evening after the tournament in the United States.
Television cameras followed their coach but the players had yet to make any comment to the media.
‘Saturated with criticism’
Messi is loved in Barcelona but his friends complained of how harshly he has been judged in his homeland.
“This lad is just saturated with criticism and being so badly treated,” said Ernesto Vecchio, who was Messi’s first coach in his native city of Rosario.
“I don’t want him to quit but when I put myself in his shoes it seems unfair that they should look to him as the savior when there are 11 players on the team.”
Messi’s cool head on the pitch makes him an efficient goalscorer, but his reserved manner has drawn criticism.
Ahead of this month’s Copa, Maradona himself accused Messi of having “no personality” for a captain.
Messi has been named FIFA World Player of the Year five times. But he has been haunted by comparisons with Maradona, who led Argentina to World Cup triumph in 1986.
The star’s departure could herald a broader change in the Argentina line-up.
Manchester City star Sergio Aguero warned other players could also quit the national side.
“We were all devastated in the dressing room, particularly Leo, I’d never seen him in such a state,” he said.
“Several players are wondering whether to continue.”
Aguero did not say whether he would follow Messi in quitting but he, Javier Mascherano and Gonzalo Higuain were mentioned in media reports.
String of defeats
Argentina were beaten 1-0 by Germany in the final of the 2014 World Cup and lost on penalties, also to Chile, in the 2015 Copa America final.
Messi also tasted defeat with Argentina in the final of the 2007 Copa America.
In this month’s Copa semi-final win over the United States, he became Argentina’s top international scorer of all time with his 55th goal.
But after Sunday’s final, his typical composure gave way to tears of frustration.
“I’ve done all I can, I’ve been in four finals and it hurts not to be a champion,” Messi told reporters.
“It’s a hard moment for me and the team, and it’s difficult to say, but it’s over with the Argentina team.”
His departure left many fans no longer thinking about the Copa.
“Losing a final is something that happens in sport,” wrote one fan, Fede Ruiz, on Twitter.
“But losing you is the most painful defeat of all.”