White House officials, buoyed by a key Democratic senator's support and the prospect of a Mideast trip by Secretary of State George P. Shultz, claimed yesterday to have the 34 votes needed to sustain President Reagan's veto of a congressional resolution blocking sales of advanced missiles to Saudi Arabia.

A senior White House official said such a trip could be politically helpful because some senators would be reluctant to stop the sale, which Reagan contends would improve U.S. relations with moderate Arab states, on the eve of a Shultz visit to Saudi Arabia.

This official said that, even if Shultz decides not to go, the administration believes that it can uphold the veto, an assessment confirmed by Sen. Warren B. Rudman (R-N.H.), an opponent of the sale.

"I think the president will win, although I must say it's not a particularly stellar way to conduct foreign policy," with backing by one-third of the Senate, Rudman said in a homestate interview with Washington Post staff writer Anne Swardson. "My basic problem with Saudi Arabia is that I don't buy it that they have been as forthcoming as the administration would believe."

In his veto message, Reagan said the Saudis, despite criticism of the U.S. raid on Libya April 15 and frequent opposition to U.S. positions, had "proven their friendship and good will" and "worked quietly" behind the scenes to reduce Mideast tension.

The Senate is scheduled to vote Thursday, soon after Congress returns from its Memorial Day recess. On May 22, Democrats succeeded in delaying the vote after Republicans claimed that they could sustain the veto.

Because the veto can be sustained by one-third plus one of senators present and voting and four senators were absent that day, only 33 votes were needed by the White House at the time.

White House officials said yesterday they reached the 34 figure after Sen. Lloyd Bentsen (D-Tex.), who had opposed the sale, called Reagan to say he would vote to uphold the veto. He is one of only four Democrats known to support the veto, which means the administration will need 30 Republicans to win if all 100 senators vote Thursday.

"We believe we have the votes now and have been working through the recess," a senior White House official said. He added, however, that the outcome remains "very tight" and said Reagan plans additional calls to undecided senators to try to offset unexpected defections.

White House officials said several Jewish leaders continue to oppose the sale even though prominent Israeli organizations have not formally lobbied against it. They also cited opposition led by Sen. Alan Granston (D-Calif.) and resistance in Texas, Louisiana and Oklahoma, where oil producers have been hard-hit by falling prices and Mideast imports.

"In this context, Bentsen's support is particularly courageous," a White House official said.

White House spokesman Edward P. Djerejian said a Shultz trip to the region, where he probably would visit Israel, Egypt, Jordan and Saudi Arabia, is in "the planning stage." But State Department spokesman Charles E. Redman said Shultz has not decided whether to go.

Shultz has been under pressure from several Middle East leaders to visit as part of a renewed U.S. commitment to the peace process but has declined to commit himself without assurances that such a journey would produce progress.

Prospects for the most likely breakthrough that could justify such a visit -- Israeli-Egyptian agreement on a disputed border area known as Taba -- dimmed yesterday when State Department legal officer Abraham D. Sofaer left the Middle East after lengthy discussions with both nations that produced less progress than had been sought.