Meloni said she was "astonished" by his comments, which were "completely made up".
She also chided him for acting with far greater deference to the enemies of the West than he does towards old, established allies.
Underscoring how much Trump's comments have angered Meloni's government, Italian Foreign Minister Antonio Tajani announced he was cancelling a planned visit to the US next week.
The latest exchange marks a sharp deterioration in ties, coming just days after signs emerged at the G7 summit that the two right-wing leaders had steadied a previously strained relationship following tensions this year over the war on Iran.
Video from the event in France showed Meloni and Trump deep in conversation, sitting side-by-side on a small sofa, but the US leader suggested he had merely indulged her by chatting with her.
"She's probably happy I talked to her. I didn't have to talk to her," Trump was quoted as saying by La7 TV channel in a brief interview, after he himself asked the journalist about Italy's prime minister.
"She begged me to take a picture with her. She wanted a picture with me so badly. I wouldn't have taken it, but I felt sorry for her," Trump said, according to La7's translation.
The channel did not release the original audio, just a dubbed version.
Meloni responded: "Donald Trump's statements are completely made up. I am frankly astonished. I don't know why the president of the United States behaves like this towards his allies: it is not the first time, moreover."
"I can only say it is disappointing that he does not show the same determination with the enemies of the West and of the United States, whose leaders he instead treats with far greater indulgence," she said.
"There is one thing he should remember: neither I nor Italy ever beg."
Announcing the cancellation of his planned US trip, Foreign Minister Tajani said on X: "The serious and offensive words of President Trump towards Prime Minister Giorgia Meloni offend the whole of Italy."
Meloni was once a vocal supporter of Trump and was the only European leader to attend his inauguration in 2025.
