As President Reagan began writing another budget last week, he was surrounded by veterans of two years of administration tax and spending battles.

But the budget deliberations also included a newcomer, Secretary of State George P. Shultz. As Reagan nears some of the most arduous fiscal decisions of his presidency, many of his senior advisers see Shultz as an important new factor in the internal White House budget debate.

"He's like the E.F. Hutton man," one senior White House official said. "When Shultz speaks, Reagan listens."

Last week's first budget overview sessions were not occasions for Shultz or others to speak out, White House officials said.

But when Shultz does make his views known, they added, he is expected to figure prominently in decisions Reagan must make in the next few weeks about the pace of his planned $1.6 trillion, five-year military buildup.

Shultz served as budget director and secretary of labor and treasury in the Nixon administration.

Now, White House officials expect him to play a mediator's role in what have been hard-fought internal battles over the Pentagon budget.

It is no secret that those battles were won, in large part, by Defense Secretary Caspar W. Weinberger, who persuaded the president not to scale back the ambitious defense expansion.

Once again, pressures are building to restrain military spending, not only from inside the administration but also from congressional Republicans and Democrats and from business groups that support Reagan's economic program but are worried about huge deficit projections.

The expectation within the White House is that Shultz will seek a middle ground for Reagan.

In this view, Shultz comes to the budget process cognizant not only of the needs of the Pentagon, but also of what some officials describe as a need for the Pentagon to help Reagan bring deficits under control.

"You can expect Shultz to argue that we need growth in the economy as well as growth in the defense budget," one official said. This view also has been privately advanced by Treasury Secretary Donald T. Regan, a close friend of Shultz.

"We know we have a serious budget problem," another administration official said after the first round of briefings on the fiscal 1984 budget last week. "Shultz is looking at it from other than bureaucratic and turf standpoints. He is taking the big picture."

"He could in the long run be very influential," a senior White House official said of Shultz, "but so far he hasn't played his cards yet."

The size of the budget "problem" is a deficit that by some internal estimates could reach more than $180 billion in fiscal 1984 without new spending cuts or increased taxes. Reagan will send the budget to Congress Jan. 17.

The president has made it clear that he intends to ask for substantial cuts in so-called entitlement spending. But that alone is not likely to make a large enough dent in the deficit, and Reagan has generally stood fast against demands that he increase taxes or crimp the military expansion that was one of his central 1980 campaign promises.

While no decisions were reached in last week's budget briefings, the internal administration debate about defense spending appeared to be intensifying. Officials stress that it is not a debate on cutting defense but on who would increase military outlays the least. Reagan's advisers are split between those who think he should remain rigid in his Pentagon requests and those who see merit in some moderation.

David A. Stockman, director of the Office of Management and Budget, is among those seeking restraint to bring deficits under control, officials said. One administration source said Stockman has been arguing that such trims from Pentagon requests will inevitably come from Congress if not from the administration and that the White House should take the lead to control the outcome.

Stockman is also emphasizing that inflation has slowed since last year so the administration can benefit from a so-called "deflation dividend," in which the same rate of growth in defense outlays can be maintained with fewer dollars, officials said.

Publicly, however, the White House position is that Reagan will accept nothing less than 7 percent growth in the military budget after inflation and may ask for more. Reagan said at his news conference last week that he would be willing to look for "savings" in military spending as long as they do not interfere with the thrust of his effort to improve defense capabilities.

Against this backdrop White House officials, including chief of staff James A. Baker III, invited Shultz to attend the budget meetings. "He's wearing his economic and budget hat, not that of the secretary of state," one administration official said.

This point was made, according to another official, when Shultz missed a budget briefing because of another commitment. The State Department telephoned and offered to send a deputy but was politely told by the White House that no one else would do, the official said.

Rather than join either side in the internal debate on defense spending, White House officials think Shultz will "mediate" differences between Stockman and Weinberger.

But they note that, had he been doing that last year, the defense budget might have been lower.

One official recalled that at a crucial point in the defense arguments last year, then-secretary of state Alexander M. Haig Jr. appealed to Reagan to support Weinberger's budget request, saying he had been a general and knew firsthand the Pentagon's needs.

"I don't think Shultz will be doing that," the official added.