WASHINGTON—Jared Kushner, President Donald Trump’s son-in-law and a senior White House adviser, said Monday he didn’t collude with any Russian efforts to interfere in last November’s presidential election and rejected any suggestion that Moscow was responsible for the president’s victory.

Speaking to reporters outside the White House, Mr. Kushner said his actions over the last two years “were proper and occurred in the normal course of events in a very unique campaign.”

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