The latest warming trend is in Pentagon-press relations

In a prominent place near the Pentagon press room is a shrine, of sorts. It is to Ernie Pyle, the famous World War II newspaper reporter who was killed in combat. In a special alcove, young uniformed tour guides point out snapshots, drawings, and personal articles recalling a time when the press and military services enjoyed a more harmonious relationship.

A few feet away are photos of the reporters now assigned to cover the Defense Department on a regular basis. Some of these people (mostly men) are military veterans themselves, and many have gained an expertise in strategy, tactics, weaponry, and defense budgets that comes from years of research and writing.

But this photo collection is less a place of honor than what some joke is a ''know your enemy'' rogues' gallery for the 26,000 military personnel and civilians who work here.

Since the Vietnam war, relations between the press and those in uniform have been strained at best.

Retired Gen. William Westmoreland's lawsuit against the CBS television network (which reported that the former commander of US troops in Vietnam had falsified intelligence data about the strength of enemy forces) makes plain that this legacy of Vietnam remains.

Not long ago, in an off-the-record seminar at the US Army War College, military officers who had begun their careers in Vietnam expressed continuing strong mistrust and in some cases bitterness about the news media as a result of their earlier experiences in combat as young lieutenants. These were the men now taking command of combat and support units and headed for top policymaking positions. A lone reporter - even though a Vietnam combat veteran himself - felt defensive and vulnerable.

Early in the tenure of Defense Secretary Caspar Weinberger, a confrontation between press and Pentagon occurred when public-affairs officers arranged a special briefing for about a dozen of the Pentagon press corps ''regulars.''

The background session was to be conducted by the Defense Intelligence Agency (DIA) and include highly sensitive classified data on Soviet military capabilities.

Before the briefing began, however, the reporters were ushered into an anteroom and told they would have to sign a ''secrecy agreement'' pledging not to ''divulge or reveal in writing, broadcast, or any verbal discourse the actual information presented at this DIA briefing nor the generic source upon which this briefing is based,'' and promising to report anybody who asked about the briefing.

The reporters balked at signing anything so sweeping, and some walked out. Pentagon officials softened the pledge to state simply that the briefing was ''off the record'' and only the source of the information could not be disclosed.

Still, the reporters refused to sign. After more negotiation, Pentagon officials no longer demanded that reporters sign anything and agreed that the briefing data could be used as background information for future stories as long as intelligence sources were not compromised. The reporters agreed.

That episode may have represented a low point in recent Pentagon-press relations, that is, until the US military operation in Grenada (invasion or rescue, depending on one's point of view) last October.

The news media were excluded from the initial landings and airdrops, and it was several days before regular press tours were allowed. Professional news organizations complained strongly, but Secretary Weinberger said he ''wouldn't dream'' of overruling military commanders on the subject of reporters going into battle.

Yet administration officials later acknowledged that the press should have been allowed into Grenada sooner. And a special committee of retired and active-duty military personnel as well as veteran journalists was formed to recommend how the question of reporters in combat could be better handled.

The results of that effort, released last week, and other improvements in Defense Department public-affairs operations indicate that smoother relations between reporters and those in uniform are developing.

In the early stages of planning for operations such as Grenada, the Pentagon now will be including ways for letting print and broadcast journalists accompany military units. Rotating pools of reporters and photographers from major news organizations (gathered on short notice) will be broadened to more general coverage as soon as security considerations permit.

''It is essential,'' said the advisory panel, headed by retired US Army Maj. Gen. Winant Sidle, ''that the US news media cover US military operations to the maximum degree possible consistent with mission security and the safety of US forces.''

Secretary Weinberger is also forming a panel of ''eminent journalists and former war correspondents'' to advise him on how best to provide press coverage of military operations.

This follows the naming late last year of a new chief Pentagon spokesman who is well liked and respected by most defense correspondents. He is Michael I. Burch, a recently retired Air Force lieutenant colonel, who has many years of experience at the Pentagon which have prepared him well for his job as assistant secretary of defense for public affairs.

Mr. Burch is straightforward, usually well informed, and handles reporters with good humor. When he doesn't know the answer to a question, he says so, often providing officers or civilian experts for background briefings.

What has thus been initiated to ease the traditional antagonism between press and Pentagon is what General Sidle's group called ''the time-tested vehicle of having reasonable people sit down with reasonable people and discuss their problems.'' The result, it is hoped, will be ''mutual respect, understanding, and cooperation in general.''