Following up on the Senate vote sustaining his veto of a trade bill, President Reagan telephoned Democratic and Republican congressional leaders Thursday to urge prompt action on a new bill to strengthen America's position in the global marketplace.

The Senate fell five votes short Wednesday of the two-thirds majority required to make the trade measure law despite Reagan's objections."The will of the Senate was expressed yesterday in sustaining the president's veto, and we are proceeding to work with the leadership in developing a new bill," White House spokesman Marlin Fitzwater said.

"President Reagan is calling a number of members Thursday to urge them to proceed as rapidly as possible on a new bill, and I think we will be able to show some movement very soon," Fitzwater said.

The spokesman declined to identify the members the president was calling but said they were "the leaders who have been involved in the development of this trade bill over a long period of time" and included both Democrats and Republicans.

Finance Committee Chairman Lloyd Bentsen, D-Texas, said he is willing to draft a new trade measure that Reagan might be willing to sign, but he acknowledged that "it's a little late in the day to be talking about a second bill."

Senate Majority Leader Robert Byrd, D-W.Va., took another tack. Although he strongly supported the trade bill, at the last minute he voted against it - a parliamentary maneuver that could later allow him to ask for reconsideration of the 1,000-page bill.

"This is insurance that the American people can still have a trade bill this year," said Byrd, who argued that efforts to draft a new measure could become hopelessly bogged down in debate over complex amendments.

Fitzwater said Byrd's action "does complicate it, and we certainly are discouraged that he would try to do that.

It is certainly clear that the president wants a trade bill; the Republicans want a trade bill; the Democrats, most of them, want a trade bill; and we would like to see it proceed as quickly as possible."

The centerpiece provisions of the bill Reagan vetoed would revamp the government's system for imposing import curbs to aid U.S. industries and retaliate against trade violations.

Others range from sizable farm export subsidies to repeal of the 1980 windfall profits tax on oil-industry earnings.

But those were overshadowed in recent weeks by Reagan's objections to a provision to require companies with 100 employees or more to provide 60-day notice of plant closings and large-scale layoffs.

The House voted overwhelmingly to override the veto last month.