The Italian premier had accused Trump on Friday of being a liar for alleging that she had "begged" him for a photo with her during this week's Group of Seven summit in France.
He repeated the assertion on Saturday, misspelling her name as "Gigiorgia" as he posted on his Truth Social platform that "she wants to be friends again in order to get her 'numbers up'".
Meloni responded with a scathing post on Instagram in English.
"President Trump, these constant, unprovoked attacks are senseless."
"My popularity is none of your concern," she added.
"I suggest you focus on yours."
Meloni's government, which took office in 2022, has seen public approval rise in opinion surveys to around 35 per cent after a steady decline in 2025.
Her Brothers of Italy party leads polls at around 28 per cent, with the opposition Democratic Party at about 22 per cent.
The US president, who was sworn in in January 2025, saw his approval rating tick up by one percentage point in recent days to 36 per cent, still near the lowest levels of his political career, as public dissatisfaction over the cost of living grew less intense, according to a Reuters/Ipsos poll.
Italy's first female prime minister told Trump on Saturday that "being his friend has certainly not helped" her popularity.
Trump repeated earlier criticism of Rome for not allowing the use of US military bases in Italy during the war with Iran that the US and Israel began at the end of February.
"Their use is governed by agreements that we have always respected and that cannot be violated. As long as I am prime minister, Italy remains a sovereign nation."
