WASHINGTON—President Donald Trump, just back from his first overseas trip as president, met privately with top advisers on Sunday and Monday as he considered changes aimed at resetting the direction of an administration beset by expanding probes into his associates’ ties to Russia.

The Trump administration is in a “perpetual quagmire on side issues,” said Chris Ruddy, of friend of Mr. Trump’s and chief executive of Newsmax Media. “There is a lot of frustration for everyone at the White House right now.”

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