President Donald Trump has retained his longtime lawyer Marc Kasowitz to serve on a team of private attorneys representing him in the special-counsel probe of his associates’ ties to Russia, two senior White House officials said Tuesday.

The move comes as the federal investigation into Russia’s alleged interference in the 2016 U.S. presidential election escalated last week with the appointment of former Federal Bureau of Investigation Director Robert Mueller III as special counsel. The move gives Mr. Mueller wide latitude...