Attorney General William Barr is sparking discord in several foreign capitals, going outside usual channels to seek help from allies in reviewing the origins of a U.S. counterintelligence investigation begun during the 2016 presidential campaign.

By meeting directly with foreign leaders—rather than relying on investigator-to-investigator channels—Mr. Barr has stirred up domestic politics in some of the countries he has tapped for assistance.

In Rome, the national-security committee of Italy’s Parliament this past week asked Prime Minister Giuseppe Conte to appear and answer questions about his contacts with Mr. Barr. Far-right opposition lawmakers criticized Mr. Conte for deferring to Mr. Barr’s request.

The Italian Prime Minister’s office said Mr. Conte isn’t worried about the meetings between Mr. Barr and Italy’s intelligence services, and said he would comment publicly only after he has been heard by the national-security committee of Italy’s Parliament.

In Canberra, Australian authorities said they were cooperating with Mr. Barr but disputed allegations that one of its diplomats acted inappropriately in 2016—an allegation at the center of Mr. Barr’s inquiry. Opposition lawmakers there, too, are expected to question government officials later this month about Prime Minister Scott Morrison’s phone conversation with President Trump regarding the inquiry.