It was a familiar morning for Mr. Trump on his favored medium — and for a nation that had, for a little more than a week, gone without the president’s stream-of-consciousness missives.

The president had largely avoided provocative Twitter posts during his journey through the Middle East and Europe, but he quickly returned to form after arriving at the White House late on Saturday, pushing back on Sunday morning against the flurry of news reports about Mr. Kushner.

“Whenever you see the words ‘sources say’ in the fake news media, and they don’t mention names,” Mr. Trump wrote on Twitter, “it is very possible that those sources don’t exist but are made up by fake news writers. #FakeNews is the enemy!”

The president woke up to find headlines and television talk shows focused on the latest turns in inquiries that he had been able to put aside for much of his trip. The freshest developments brought the matter into his own family.

News articles also focused on efforts by administration aides to develop a damage control plan to handle the controversies. That plan would potentially seek to wall off questions involving the investigations from day-to-day governing by creating a separate war room in the White House, assembling a high-powered legal team outside the White House and shaking up the president’s communications team.

Aides expected Mr. Trump to begin meeting with lawyers as early as Sunday to talk about a way forward, but one consensus among administration lawyers and private lawyers consulted by the White House in recent days was that Mr. Trump needed to restrain himself on Twitter, rather than create new problems with impulsive or unfiltered messages.

Mr. Trump demonstrated during his travels to Saudi Arabia, Israel, the West Bank, the Vatican, Belgium and Italy that he could be disciplined about his use of social media. Over the nine-day trip, he or his aides used the president’s Twitter account to promote his foreign and domestic policies, thank his hosts and otherwise stay on message.