WASHINGTON — At 9:34 on the November morning after Donald J. Trump was elected president in 2016, Kirill Dmitriev, the head of Russia’s sovereign wealth fund and an informal envoy for President Vladimir V. Putin, sent a text message to a Lebanese-American friend with ties to the Trump campaign.

Mr. Dmitriev wanted to connect quickly with someone in Mr. Trump’s inner circle, preferably Donald Trump Jr. or Jared Kushner. By the end of the month, he was in touch with Rick Gerson, a friend of Mr. Kushner’s who manages a New York hedge fund.

The two discussed a potential joint investment venture. But the special counsel’s report released Thursday suggested that Mr. Dmitriev’s real interest lay elsewhere: He had been instructed by Mr. Putin, he told Mr. Gerson, to come up with a plan for “reconciliation” between the United States and Russia.

Mr. Dmitriev and Mr. Gerson worked together on a two-page proposal for how the nations could cooperate on a variety of fronts. That document, the report said, later made its way to Mr. Kushner, Rex W. Tillerson, the incoming secretary of state, and Stephen K. Bannon, Mr. Trump’s chief strategist. Nothing came of the idea that the Russian sovereign fund would invest with Mr. Gerson.