The Italian PM said the pact, which happens every five years, would be suspended "in view of the current situation".
Meloni vowed to press on after losing a vote on constitutional reform many turned into a referendum on her government.
The dry subject matter of this weekend's vote seems obscure but for many it is a vote on the PM.
European nations say they want to work better together but have differing priorities
The artist has denied modelling the fresco on the prime minister.
Europe is split between hitting back at Trump's tariff threat or holding fire to avoid a damaging trade war.
Pro-Palestinian marches gripped Italy's cities on Friday, defying the right-wing government of Giorgia Meloni.
Leading Italian politicians spoke out against the site, which blamed the "toxic" behaviour of its users.
For now the Holy See says the idea of even hosting talks is more a hope than a concrete plan.
