President Reagan yesterday directed changes in the rules governing travel by executive branch employes that are designed to cut about $200 million from this year's estimated $4 billion travel bill.

More than half the savings would come from a new requirement that federal travelers buy their airline tickets from government travel offices or commercial travel agencies to assure maximum use of discount fares -- those provided under government contracts with the airlines as well as those generally available.

The White House directives came as the General Services Administration announced it has awarded new one-year contracts to a dozen airlines to carry federal travelers at discount fares on 45 different routes. GSA estimated that the contracts are worth about $4.5 million to the airlines and will save the government about $2.3 million over commercial fares.

As examples, Ivan Michael Schaffer, assistant commissioner of GSA's office of transportation and travel management, said federal employes will be able to travel from Washington to Albuquerque on Texas International Airlines for $182, compared with an average coach fare of $347; to Atlanta on Eastern Airlines for $104, compared with the average coach fare of $142.50, and to Boston on Braniff International, New York Air to Northwest Airlines for fares raning between $37 and $49 one way, compared with an average coach fare of $96.

Altogether, GSA has awarded contracts worth $74 million to 18 airlines for service to 157 cities since it began the program in May, 1980.

GSA Administrator Gerald P. Carmen yesterday also announced the expansion of an experimental program to use commercial travel agents to arrange trips for federal employes. Contracts will be awarded this fall for agents in Denver, Washington and Dallas/Fort Worth.

Right now, most federal travel is booked through Scheduled Airline Ticket Offices, offices staffed by the airlines but located in the agencies. According to GSA and other sources, this doesn't always work to the government's advantage. Recently, for instance, United Airlines, which manages some of the offices, canceled its ticketing agreement with New York Air. The result is that the ticket offices that use United's computer reservations system can no longer write tickets for New York Air flights, even though it is one of the airlines federal employes are supposed to use for travel between some cities.

GSA's Schaeffer also pointed out that these ticket offices have no built-in incentive to save money for the government by writing low-cost tickets. Under the new program, a commercial travel agent under contract won't get commissions for writing federal air travel tickets but will be able to get commissions on hotel and auto rental bookings and on any tickets booked for employes' private travel.

Government agencies were also directed by the White House to tighten travel authorization policies, partly by reducing the use of general travel authorizations. Last year, the Office of Management and Budget did a survey of 1979 travel vouchers and authorizations and found it couldn't discern the reasons for 27 percent of the trips. Accumulating the information in a different way, a survey conducted this year by GSA of 1980 travel found that the government could account for all but 4.9 percent of the 14.3 million trips taken.