Conte was commenting from the G7 summit in Canada, where the leaders of Italy, France, Germany, the UK, Japan, Canada and the US are gathered for top-level talks.
Screenshotting a headline about US President Donald Trump's suggestion that Russia be invited back to the group of nations, Conte tweeted: "I agree with President Trump: Russia should return to the G8. It's in everybody's interest."
The US president had earlier called for Russia – which was suspended from the group in 2014, following Moscow's annexation of Crimea, and decided to leave permanently in 2017 – to be readmitted in the interests of realpolitik.
"Whether you like it or – and it may not be politically correct – but we have a world to run and in the G7, which used to be the G8 they threw Russia out, they should let Russia come back in," Trump said upon his arrival in La Malbaie, the small town in Quebec that is hosting the weekend's summit.
Conte's decision to side with the US may irritate his European allies, who have so far declined to make any overtures to Russia – though previous Italian governments have expressed hopes that Russia would one day return, as has Japan.
The Italian prime minister was due to meet the leaders of France, Germany and the UK before the main summit in a session seen as a European "huddle" designed to present a united front to President Trump, who has imposed trade tariffs on the EU and disagrees with the bloc over a nuclear deal with Iran.
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Conte's statement is one of the earliest clues as to what the new Italian government's foreign policy will be as Conte, who was sworn in one week ago, attends his first international meeting. So far the prime minister has said only that Italy remains a committed member of Nato and a special ally of the US, and that he will push for a review of sanctions against Russia.
It's also the first time that Conte has used his Twitter account – which features just seven tweets to date – to make a policy statement. The premier's governing style is a total unknown, since he had never held public office before being appointed a compromise prime minister by Italy's governing coalition.
Italy has long been considered one of the most pro-Russia members of the European Union. Its trade ties with Russia are worth several tens of billions of euros each year, while several leading figures in both the Five Star Movement (M5S) and the League, the two populist parties that make up the coalition government, have expressed personal admiration for President Vladimir Putin. Matteo Salvini, head of the League, interior minister and deputy prime minister, has even met him personally in Moscow.
Speaking on Friday, Italy's other deputy prime minister, Luigi Di Maio of the M5S, said that sanctions on Russia "damage" Italy.
"We are pro-Italian, not pro-Russia," Di Maio told a radio interviewer, while stressing that Conte would make his own decisions when representing Italy on the world stage.
League leader Matteo Salvini, who has been to Moscow several times. Photo: Giuseppe Cacace/AFP