WASHINGTON—President Trump’s stop-and-start trade policy and uneven economic messaging have rattled some of his own allies, triggering a flood of calls from business executives, concerns from Republican lawmakers and tension in the White House.

Senior officials, including White House chief of staff Susie Wiles, have received panicked calls from chief executives and lobbyists, who have urged the administration to calm jittery markets by outlining a more predictable tariff agenda, according to people familiar with the discussions. Many in the business community have abandoned efforts to get the president to reverse course on trade, instead pleading with the White House for clarity on his approach, the people said.