Mr Kalifat said it was "an insult" that a French president could honour Petain on "the same level as the other generals", but he acknowledged the marshal's pivotal role in the Great War that earned him the nickname "Lion of Verdun".
"I consider it entirely legitimate that we pay homage to the marshals who led our army to victory".
May's visit is part of the commemoration of the First World War that has led Macron's week-long tour through battlefields in France.
"He was a great soldier, it's a fact, he added, though he stressed that Petain had made "disastrous choices" during World War II".
Critics were quick to criticize Macron, pointing to the role that Petain played in history later in life.
The French presidency later said that only the five top military chiefs who are interred in the Invalides will be individually honored and have their names cited in the ceremony -not including Petain.
Macron, who has spent the past week touring former battlefields of eastern and northern France, met May in Albert near the Belgian border for a working lunch as pressure to reach a deal on Britain's European Union exit mounts.
But Wednesday's remarks struck a deep chord in a nation that has lived through two world wars and only in recent decades has acknowledged its collaborationist past.
But as head of the Vichy regime, he actively collaborated with the Nazi occupiers, pursuing French resistance fighters while enacting second-class status for Jews and helping German soldiers round them up for the death camps.
His comments were denounced by rival politicians and Jewish leaders, and set off a flurry of criticism on Twitter. "It judges the huge and unworthy responsibility of a marshal who deliberately used his name and prestige as a cover for treason and the collaboration and deportation of thousands of Jews in France".
"The only thing we will remember about Petain is that he was convicted, in the name of the French people, of national indignity during his trial in 1945", Kalifat said in a statement.
The ceremony is another symbol of reconciliation between France and Germany, as Rethondes was also the site imposed by Nazi Germany on the French when accepting their surrender in 1940 during World War II, the Elysee said.
"Every aggression perpetrated against one of our citizens because they are Jewish echoes like the breaking of new crystal", the French prime minister wrote on Facebook, referring to the start of the Nazi drive to wipe out Jews on November 9, 1938, also known as the Night of Broken Glass.
After the war's end he was arrested for treason and given the death sentence, which was commuted into life imprisonment given his age.
Jean-Luc Mlenchon, leader of the far-left party France Unbowed, tweeted: "Macron, this time you've gone too far!"
French army officials had announced that all eight WWI marshals would be commemorated at the Invalides military hospital and museum in Paris on Saturday.