Mr. Trump’s comments Monday were the latest by him, his aides or his associates that suggest a desire to disrupt that consensus, a desire that has seemingly deepened as they find more ideological allies in Europe to work with.

Earlier this month, Mr. Trump’s new ambassador to Germany, Richard Grenell, said he wanted to “empower” right-wing figures across Europe. And if there is one issue on which Mr. Trump can make common cause with his new allies, it may be immigration.

It is too early to say whether Mr. Trump’s scattershot outbursts are the harbinger of a settled strategy, said Jeffrey Rathke, a former senior United States diplomat who served in several missions in Europe.

“But there is certainly an increasing body of evidence that Trump and his representatives are trying to find ways of strengthening those right-wing forces in Europe that oppose the E.U. playing a strong foreign policy role,” said Mr. Rathke, deputy director of the Europe program at the Center for Strategic and International Studies, a Washington think tank.

Two days before his seeming glee on Twitter about Ms. Merkel’s travails, Mr. Trump spoke by telephone for the first time with Prime Minister Viktor Orban of Hungary, who has spent eight years in Budapest building an “illiberal democracy.”

Mr. Orban has called for “a countercultural revolution” against the Continent’s liberal order. He has led the campaign to turn back migrants from Europe’s borders. As Ms. Merkel argued for a more compassionate response to the crisis in 2015, the Hungarian leader built a fence along his country’s southern perimeter.