At White House urging, the Senate has broken its hard-and-fast moratorium on new federal construction so President Reagan can make a gift to Mexico this week.

In return, Senate horse-traders got a White House commitment to presure the House to pass a stalled bill that would revise federal construction policies.

The gift is approval of a $13.3 million border-crossing station four miles east of San Diego, to ease traffic jams between Mexico and California.

Approval had been held up by the Senate Environment and Public Works Committee's effort to reshape construction policy and halt the traditional building-by-building approach.

The committee allowed a one-time-only exception to its moratorium after Chairman Robert T. Stafford (R-Vt.) said a presidential appeal and a letter from White House counselor Edwin Meese III called the border station vital to U.S.-Mexican relations.

Reagan is scheduled to meet with Mexican President Jose Lopez Portillo tomorrow and Tuesday and, according to Meese, wanted to be able to report approval of the Otay Mesa station.

Stafford told the committee he had agreed to waive the moratorium with the understanding that the White House would support the Senate-passed legislation revising construction policy.

"They [the White House] completely support the committee and will exert considerable pressure on the House to pass the bill," Stafford reported.

"It is a courtesy we should give the president on foreign affairs," said Sen. Daniel Patrick Moynihan (D-N.Y.), co-author with Stafford of the bill. "You have bargained very well."

An aide to Sen. Alan Cranston (D-Calif.) said approval of the crossing station figures prominently in Mexico's plans to develop an area just south of the border with the United States.

Mexicans may applaud Meese's letter to the committee stressing the administration's effort to improve relations with Mexico, but if they saw the letter itself, they might surmise the administration has a way to go.

The letter twice referred to President Jose Lopez Portillo as Portillo. His surname is Lopez. The custom in Mexico is to put the mother's family name after the father's.