WASHINGTON — The White House is pushing to issue an order that would designate the Muslim Brotherhood a foreign terrorist organization, bringing the weight of American sanctions against a storied and influential Islamist political movement with millions of members across the Middle East, according to officials familiar with the matter.

The White House directed national security and diplomatic officials to find a way to place sanctions on the group after a White House visit on April 9 by President Abdel Fattah el-Sisi of Egypt, for whom the Brotherhood represents a source of political opposition. In a private meeting without reporters and photographers, Mr. el-Sisi urged Mr. Trump to take that step and join Egypt in branding the movement a terrorist organization.

Such a designation imposes wide-ranging economic and travel sanctions on companies and individuals who interact with the targeted group. The president responded affirmatively to Mr. el-Sisi, saying it would make sense. Some of Mr. Trump’s advisers have interpreted that as a commitment, officials said.

But the proposal has prompted fierce debate within the administration, including at a senior-level meeting of policymakers from various departments convened last week by the White House’s National Security Council, the officials said.