The White House is on the verge of invoking a claim of executive privilege to prevent the release of 18 documents in connection with a civil lawsuit that alleges there was high-level political interference in a decision to block a Federal grant to a Texas anti-poverty organization.

The suit alleges that White House aides, seeking to placate Texas Gov. Dolph Briscoe and members of the Texas congressional delegation, pressured the Community Services Adminsitration into blocking release of a $855,000 grant to the Zavala County Economic Development Corp.

The Mexican-American organization, located in the South Texas community of Crystal City, has feuded frequently with Briscoe.

At a brief hearing yesterday before U.S. District Court Judge Gerhard A. Gesell, William Z. Elliott, a Justice Department lawyer representing the White House, said a claim of executive privilege by President Carter is "a definite possibility" in the case.

In the meantime, the White House has refused to produce the documents on the grounds that they involve privileged attorney-client communications and "intra-governmental privilege," a legal concept that Gesell said yesterday he did not understand.

The case has confronted the Carter White House with a delicate political situation. Executive privilege - a claim that certain documents belong to the president and he may not be compelled to surrender them - was widely invoked in the Nixon White House in connection with the Watergate case.

Given Carter's repeated public, commitments to "open government," it would be politically embarrassing for him to use a tactic so closely associated in the public mind with the Nixon era.

But White House lawyers will have to weigh that factor against the contents of the documents, which include several memoranda from staff aides to the president.

A listing of the documents being sought by Noel H. Klores, the lawyer for the Texas group, was filed in court yesterday. The list indicates there was an unusually early and high-level interest in the White House in a relatively insignificant government grant.

On Jan. 28, 1977, after he had been in office only eight days, Carter received three separate memoranda on the Zavala grant. One was from White House counsel Robert Lipshutz and his deputy, Margaret McKenna. The others were from congressional relations chief Frank Moore and Joseph Aragon, an aide to Hamilton Jordan, the president's chief political adviser.

The next day, according to the listing, Attorney General Griffin B. Bell advised the president in writing on "the procedures applicable to suspension and/or termination of OEO [Office of Economic Opportunity] grants" such as the Zavala grant. By the end of February, 1977, Carter had received eight memoranda, most of them from Aragon, on the subject.

Aragon is a key White House link to Hispanic-American organizations who has worked with Jordan on such matters as appointments.

The White House initially refused to produce the documents last week when depositions were taken in the case from Moore, McKenna and Aragon. The three presidential aides were questioned about a meeting they attended at the White House last September with Graciela Olivarez, the head of the Community Services Administration.

The meeting concerned the Zavala grant and congressional relations and was according to court documents, the only time Olivarez has been summoned to the White House to discuss one of her agency's grant applications.

In court papers, government lawyers have denied any political interference in connection with the grant. Gesell yesterday set April 7 for a hearing on release of the documents being sought by the Zavala group.

Washington Post staff writer Timothy S. Robinson contributed to this article.