The State Department, always on the lookout for ways to isolate further the government of Cuban President Fidel Castro, has stumbled into a fight with Walter Cronkite and CBS News while avidly pursuing its policy of limiting U.S.-Cuban links.

Thursday afternoon, the department refused permission for CBS to use international satellite facilities for the broadcast of a two-minute report from Havana on the growing economic problems confronting the Castro regime.

State Department officials ruled that the report did not involve a "specific event of immediate international importance" and was therefore not eligible for an exemption from the U.S. embargo against Cuba as has been granted in the past to allow television news broadcasts by satellite from Cuba.

Last night, when the time CBS had reserved with the COMSAT Corp., the private firm that operates the satellites, for transmission of the report to New York passed without word from the State Department, the item again failed to appear on the CBS Evening News.

State Department officials said yesterday that the dispute and the policy on broadcasts from Cuba "are now being studied intensely at the highest levels of the department."

Meanwhile, CBS officials reacted with outrage.

"CBS News believes that news should be free to move out on satellites all over the world divorced from political considerations," said Bill Leonard, the network's news division president.

The dispute involves not only CBS and the State Department, but also COMSAT, the Treasury Department and the Federal Communications Commission.

The U.S. trade embargo, imposed against Cuba in 1963, precludes upgrading of any links between the United States and Cuba, including communications links. Satellite communication fell under the embargo last September, when Cuba obtained the necessary ground station facilities to hook into the international satellite system and invited U.S. television networks to Havana to report on a meeting of nonaligned nations there.

It was then that ther State Department began granting exemptions from the embargo to allow satellite broadcasts of television news reports. More than 20 exemptions have been granted for reports on such events as the massive anti-American demonstration in Havana on May 17 and the status of Cuban refugees waiting at Mariel harbor for boats to take them to Florida.

COMSAT, which represents the United States in the INTELSAT global communications system, must receive permission from the FCC before it accepts transmissions from Cuba. The FCC, in turn, routinely consults with the Treasury Department, which administraters the trade embargo, and the State Department before granting permission.

And it was the State Department that Thursday said no to CBS, stranding the report by the network's Latin American correspondent, Charles Gomez, in Havana. Instead, CBS broadcast a report on the rejection and the dispute by correspondent Fred Graham.

State Department spokesman Hodding Carter yesterday confirmed the government's action that set off the dispute. He said the department did not want to get into the business of reviewing the content of news broadcasts, but added:

"However, the policy, as opposed to the exceptions, remains to deny satellite hookups covering nonspecific events such as a news special on Cuba involving several days of shooting. These types of stories can be continued to be provided through other means."