The Department of Transportation said yesterday it has decided not to investigate whether Trans World Airlines' operating fitness would be impaired if New York financier Carl Icahn takes over the carrier.

TWA had asked the agency to consider lifting TWA's certification as an airline if Icahn succeeded in gaining control of the carrier.

The department, reflecting a philosophy also followed recently by other government agencies asked to arbitrate takeover battles, said it did not want to be "drawn into takeover attempts or other management disputes as a matter of course, or to otherwise substitute unnecessary government regulation for the competitive pressures of the marketplace."

In addition, the department said, "TWA has not provided a compelling justification for a DOT investigation of the airline's or Icahn's fitness at this time."

The decision is a blow to TWA's attempts to fend off the advances of Icahn, who owns about one-third of TWA's stock and is offering about $400 million for the rest. TWA can, however, ask the DOT to reconsider its decision. The airline had no comment yesterday on the DOT's action, although a TWA spokesman said, "We have seriously questioned Mr. Icahn's fitness to run TWA and continue to question it."

TWA is still ahead on another legal front in the battle: State courts in Missouri, where the company is incorporated, have so far upheld a recently passed Missouri law that effectively blocks Icahn from gaining control of TWA. Under a temporary restraining order obtained by TWA, Icahn is prevented from furthering his attempt to take control at least until next Monday, when a Missouri court will consider a permanent injunction against Icahn's attempts.

TWA also is reported to be negotiating with a possible "white knight," Resorts International Inc., to make an offer for the airline higher than Icahn's $18-a-share bid. TWA has said that if it does not get an offer better than Icahn's before the end of July, it will take Icahn's offer to shareholders for a vote.

The airline filed a request with the DOT four weeks ago asking that the department consider decertifying it in the event of a takeover by Icahn because it claimed that Icahn was "unfit to be entrusted with the control of a large air carrier like TWA." The airline based its arguments on Icahn's lack of experience running airlines, his past run-ins with the Securities and Exchange Commission, and his record as a Wall Street raider.

But the Transportation Department said TWA had failed to demonstrate a "compelling lack of fitness" on Icahn's part. The department said it would need evidence of both a lack of fitness and a "strong" likelihood of a change in control to lead it to consider decertif