President Carter, continuing his public display of concern over secrecy and special privilege in government, told his Cabinet secretaries yesterday to reduce their travel expenditures and said he is considering opening regular Cabinet meetings to some form of press coverage.

The President, who last week ended the tradition of providing home-to-work limousine service for senior presidential aides, told the Cabinet members he wants them "to do the same" regarding limousine service for high-ranking officials in their departments. He also told the Cabinet secretaries "to cut out the ostentatiousness" of their own travel around the country and abroad.

"I hope you'll go the extra mile," Carter said. "I don't want to be superficial about this."

At yesterday's opening of the second regularly scheduled Cabinet meeting of the administration, the President announced a "tentative" decision to open future meetings to the press. But he made clear that the details of such coverage are yet to be worked out and that he would want some limits on what was reported.

Calling the first Cabinet meeting of the Carter administration "absolutely superb and possibly unprecedented," Carter said that opening future meetings to the press would "let the American public know their government is in good hands."

It is likely that any future news coverage of Cabinet meetings would be done by a small "pool" of reporters who would then report to the full White House press corps.

The President also noted that some Cabinet secretaries might feel "constrained" about making proposals in the presence of reporters. He suggested, as a possible solution to this, an agreement by the press not to attribute comments to specific persons. Such ground rules must still be worked out between the White House and representatives of the press, he said.

To open Cabinet meetings to the press would be a radical departure. But it also appeared that Carter's suggestion could run counter to his own often-stated determination to have an independent Cabinet whose members did not fear expressing their own views.

Most government officials argue that sensitive matters must be discussed in private or else the participants, in the President's own words, feel "constrained" about expressing themselves. Moreover, when government meetings are open, the most sensitive topics frequently are discussed and decided in other forums, out of public view.

A White House official, who asked not to be identified, conceded that this would be the likely result if Cabinet meetings are opened to the press. Such items as "personnel matters" and "legislative strategy" would have to be discussed in a separate and, in effect, private Cabinet meeting, he said.

Asked what purpose would be served by press coverage of Cabinet meetings when many of the most important matters remained private, the official replied, "I don't know."

Carter's comments at yesterday's Cabinet meeting were relayed to reporters by deputy White House press secretary Rex Granum.

Speaking of his desire to reduce the cost of government, the President recalled that in the early stages of his election campaign he flew tourist class on commercial airlines. Although no order to follow that example has been issued, Granum said the message to the Cabinet "seemed pretty clear."

Carter also said that he personally rejected a Secret Service request to provide security-equipped limousines to Vice President Mondale for his trip to Western Europe and Japan. Mondale's ground transportation has been provided by the host governments.

The President said that while he shares the "natural inclination" to accept special services and conveniences available to him and the Cabinet, "I want to cut back on that drastically."

Granum spent considerable time reporting the discussion of limousines and other privileges, providing exact quotations from Carter and others. Asked how much time was devoted to such matters in the 2 hour and 20 minute Cabinet meeting, he replied, "About 10 minutes."