The House yesterday approved a $2.5 million budget for its assassinations inquiry by an unexpectedly slim margin. The vote was 213 to 192.

Rep. Louis Stokes (-Ohio), chairman of the House Assassinations Committee, told reporters that the slippage in support was probably due to last weekend's statements by Del. Walter E. Fauntroy (D-D.C.) about a possible investigation of some reporters covering that inquiry.

Fauntroy said in a weekend television interview that he was annoyed by news reports that that committee has come up with nothing new thus far and said he thought it possible that some of the reporters were Central Intelligence Agency employees out to destroy the investigation.

Pressed for an explanation on the House floor yesterday by Rep. Robert E. Bauman (R-Md.), Fauntroy said the Assassinations Committee "has no plans, current or future, to call news reporters before it for purposes of probing their coverage of the investigation."

But he added that he had "a personal interest in finding out whether certain news reporters have been influenced by reasons other than providing information to the public."

Asked later which stories bothered him. Fauntroy declined to be specific saying. "There are so many." He indicated that he still hopes to find out whether any reporters writing about the committee were among the three dozen unidentified American journalists the CIA once used and paid as undercover contacts while they were working as foreign correspondents.

Urging that the committee be denied any more money. Bauman maintained that the House was really "voting on the conduct of the committee" since it was reconstituted last month for the remainder of the 95th Congress by a 230-to-181 vote.

Rep. John H. Dent (D-Pa.), who managed the floor debate as chairman of the House Administration Accounts Subcommittee, argued, however, that the House had already decided to go ahead with the inquiry into the deaths of President Kennedy and the Rev. Martin Luther King Jr. and that the only question now was an adequate level of funding.

He pointed out that the $2,514,400 resolution for 1977 was far below the $6.5 million the Assassinations Committee proposed last winter on the recommendation of former chief counsel Richard A. Sprague.

Stokes, it was learned, recently met with former Watergate special prosecutor Archibald Cox to sound him out about the job of chief counsel for the committee and get his advice on any other possible candidates. Fauntroy said he doubted that the Harvard professor would take the position, but "he (Cox) said he would think about it and others' who might be considered. Cox could not be reached for comment.