Bruce Smart resigned yesterday as undersecretary of Commerce in charge of international trade after Commerce Secretary C. William Verity said he no longer supported Smart's promotion to deputy secretary, the number two job in the department.

In a statement last night, Verity said, "A difference of management styles developed between Bruce Smart and myself and I asked him to agree to have his name withdrawn for the position of deputy secretary. I thought that he had done a superb job as undersecretary for international trade and I asked him to continue in that position.

"However, he declined and to my regret has submitted his resignation to the president," Verity said.

The resignation comes at an awkward time for the department, which is still trying to regain clout within the administration that it lost when Secretary Malcolm Baldrige died in a rodeo accident last July.

Furthermore, Smart, who was a leading candidate from inside the department to replace Baldrige, was slated to play a major role in administration negotiations with Congress over the shape of a major trade bill. "With the trade bill coming on, this is not good," said an administration official.

The resignation came as a surprise to the White House and other Commerce officials. Smart's name had been submitted to the White House for promotion to deputy secretary and candidates were lining up to succeed him in the undersecretary's job. While the promotion had not been fully cleared in the White House or Congress, it was considered "pretty much a done deal," an official said.

Late last week, however, while Smart was out of Washington on business, sources said that Verity changed his mind and asked the White House to withdraw Smart's name from consideration. When Smart returned to the office Friday afternoon, sources said, Verity told Smart he was no longer wanted as chief deputy, but asked him to stay on as undersecretary.

"He couldn't stay. He was perceived as having lost the confidence of the secretary," said an administration official.

Smart was picked by Baldrige to take the highly visible job as undersecretary in charge of international trade almost three years ago after a career as a corporate chief executive. He lost his last job as head of Continental Can Co. after that firm was taken over in a merger.

Smart was the Reagan administration's point man on many contentious trade issues, including the battle to get Japan to open $60 billion in planned public works projects to U.S. engineering and construction firms.

It is unclear who will succeed Smart. Sources said there were four main candidates if he had become deputy secretary. They are J. Michael Farren, the deputy undersecretary; Charles E. Cobb Jr., assistant secretary for trade development; Donna C. Tuttle, undersecretary for travel and tourism and wife of Robert H. Tuttle, head of the White House personnel office; and Jan W. Mares, who works in the White House Office of Policy Development.