WASHINGTON — The White House said Tuesday night that it would refuse to allow its director of political strategy to testify Wednesday before a Republican-led House committee investigating whether the administration had illegally conducted political activity in the West Wing.

In a letter to Representative Darrell Issa, the chairman of the House Committee on Oversight and Government Reform, the president’s top lawyer said that as a member of the executive branch the political director, David Simas, had immunity from being compelled to testify before Congress.

Mr. Issa’s committee subpoenaed Mr. Simas last week, contending that the White House should not have opened the Office of Political Strategy and Outreach this year. Mr. Issa told the White House in May that “the American people have a right to know if their tax dollars are being spent to support congressional campaigns during the 2014 midterm elections in violation of federal law.”

In a statement on Tuesday, Mr. Issa said that the decision to prevent Mr. Simas from testifying was “another attack on our nation’s Constitution” and that he planned to examine whether the president intended to assert executive privilege.