The State Department yesterday renewed its request for American firms to leave their operations in Libya after American and Libyan jet fighters clashed over the Mediterranean, but many of the companies said they didn't expect any trouble from the Libyans and had no immediate plans to leave.

"We work pretty much like the Jesuits do," said Robert Caplinger, a vice president for Raymond International Inc., engineers and builders. "We bring in a small cadre of people and hire indigents." Raymond officials told the State Department yesterday morning that none of its eight employes currently working on construction and engineering jobs there is an American.

Steven Christian, president of Christian International Ltd., which repairs and maintains oil wells, said he spoke with his father and brother yesterday in Libya and they said "everything was just normal." Christian has 70 Americans working in Libya and doesn't plan to withdraw them.

Last June the State Department advised American firms to leave Libya following the Reagan adminsitration's decision five weeks earlier to close the Libyan diplomatic mission in Washington. The firms chose to ignore the warning, saying that the Libyan government assured them that it planned no retaliation against American firms. Officials of four of the six American oil firms operating in Libya said they resented being asked to carry out Washington's political decisions.

But following the dogfight yesterday between Libyan and U.S. planes over the Mediterranean, the State Department renewed its request that American firms leave.

"The company's view is that this is a dispute over territorial airspace," a spokeswoman for Occidental Petroleum Corp. said. "It's a political matter rather than a commercial situation."

"We have about 12 people there, all told," said a spokesman for Conoco Inc. "Our production operations are normal as of now."

Brown & Root International Ltd. has 79 employes working in Libya. Six employes are working on engineering and contract management of a water pipeline, 3 are maintaining contracts on existing projects and 70 others are working on a construction management project for a refinery, according to James Harper, assistant director of public relations.

"We're waiting to see what does happen," Harper said. The firm has no immediate plans to leave the country.

"We've been in touch with our people over there,"' said Bill Smith, a spokesman for Exxon Corp. in Washington. Smith said the company is "not aware of any problem" and it is "following the situation closely." Exxon has 85 employes with 115 dependents in Libya.

The Commerce Department estimates about 2,000 Americans are living in Libya.