Macron said in an interview Wednesday with French television TF1 from the Charles-de-Gaulle aircraft carrier off the coast of southern France that "the French don't expect from me to answer to tweets".
The US president's call to "make France great again" also came in for mockery from Benjamin Mendy, the Manchester City defender who was in France's World Cup winning football team.
While the French president insisted the reference to the US was only to imply that Europe needed to rely less on the US, Trump launched into a days-long tirade against Macron and France.
When asked by a reporter about the tweets, Macron said, "At each important moment in our history we have been allies, and between allies there is respect and I do not want to hear the rest".
"Emmanuel Macron suggests building its own army to protect Europe against the US, China and Russian Federation. And to do this, we can not depend on (others), including the United States".
But asked whether there was a deeper misunderstanding between the two countries after Mr Macron's comments about a European army infuriated Mr Trump, the French President said being a USA ally did not mean being subservient.
"It's the ally with which we take all the risks, with which we carry out the most complicated operations".
French President Emmanuel Macron looks on during World War I commemorations at the Douaumont Ossuary near Verdun, in northeastern France, on November 6.
The battles with May and Macron are the latest example of Trump's abrasive style when meeting worldwide leaders. It's true, as Mr. Trump took delight in pointing out, that Mr. Macron's approval rating is now as low as those of his two immediate predecessors, Nicolas Sarkozy and François Hollande, who both ended up as one-term presidents.
"Pay for North Atlantic Treaty Organisation or not!"
"We were commemorating the assassination of 130 of our compatriots three years ago in Paris and Saint-Denis, and so I will reply in English: "Common decency" would have been appropriate", Griveaux said.
Macron and Trump initially enjoyed a close relationship, but disagreements on a series of topics has seen "Le Bromance" deteriorate.
May had argued before that Iran is meeting all its obligations under the 2015 JCPOA nuclear deal despite Trump exiting the agreement and reimposing sanctions.