Italian Prime ​Minister Giorgia Meloni says President Trump is full of crap ... because there's no way she "begged" him for a photo together at the G7 summit, despite Trump's claim.

The PM posted a video on social media expressing her disgust ... claiming Trump is just spinning lies ... saying, "There is one thing he should remember: neither I nor Italy ever beg."

Meloni's response comes after Trump said she "wanted a picture with me so ​badly ... I wouldn't have taken it, but I felt sorry for her" ... Reuters reports Trump made the comment to an Italian TV station.

Trump and Meloni used to be close, but the world leaders had a major falling out over the Iran War ... hence the bitchiness now.

Meloni was clearly pissed about the comment, zinging Trump again ... "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."

That's not amore!!!