Western Union Telegraph Co.'s monopoly on domestic telegram service, granted in 1943, is about to be reviewed for the first time by the federal government.

A formal investigation of the monopoly was ordered yesterday by the Federal Communications Commission, as the agency permitted a potential Western Union competitior to begin offering facsimile message delivery services between U.S. points and overseas markets.

Graphnet Systems Inc., a subsidiary of Graphic Scanning Corp. that won the limited FCC authority yesterday, also has been seeking regulatory approval to distribute international data and facsimile transmissions from abroad to U.S. markets.

Western Union and other communications firms opposed the new competition and, pending the outcome of the FCC's inquiry, Graphnet Systems was denied authority to deliver messages in the U.S.

In related decisions yesterday, the FCC:

Ordered hearings on a Western Union proposal to earn by 1981 a 23 percent rate of return on investment in its TWX and Telex message communications services; the current rate of return is about 18 percent, FCC officials said. Relatively high profits from such business services subsidize less profitable and dwindling private telegram services, according to Western Union.

Granted authority to a Washington company, Telenet Communication Corp., to offer certain private data communications services between U.S. cities and overseas.

Western Union's domestic telegram monopoly was sanctioned by the FCC when the agency approved a merger of competitor Postal Telegraph into the surviving firm because both were having financial difficulties in a competitive environment.

But the FCC yesterday concluded that new technologies and services, as well as new attitude in favor of competition, had changed "the factual situation . . . significantly."

Specifically, the agency ordered an investigation to determine if competition should be allowed in U.S. public telegraph services, what new regulatory standards and procedures would be required for oversight of a competitive maketplace and the economic impact of competition for Western Union.

In opposing the bid by Graphnet Systems to deliver messages in this country from overseas points, Western Union told the FCC that its potential competitor would be engaging in "cream-skinning" - taking away profitable business on a pick-and-choose basis while leaving Western Union with a mandate to serve less profitable markets.

Western Union charged that Graphnet might reduce the established firm's annual revenues by as much as $7 million, and that profits could be reduced by up to 20 percent. The only options in such an event would be to increase rates or reduce quality of services "upon which many small non-business customers depend," Western Union stated.

In rebuttal, Graphnet said its proposed service would rob Western Union of only $660,000 in revenues a year after three years of implementation with one international carrier, and a maximum of $2.4 million if connections are provided with all international carriers.

Graphnet also charged that, by offering other services on its own, Western Union had diverted revenues from its telegram monopoly.

The FCC will seek public comments for its Western Union inquiry by dates to be announced in the near future.