Taxicab rates will go up a week from Monday by a bit more than 10 percent for passengers who ride District of Columbia cabs between Washington and places in Maryland and Virginia, including National Airport.

The fare increase, designed to keep the cost of an interstate ride in an unmetered District cab at about the level of a ride in a metered suburban cab, was approved in an order circulated yesterday by the Washington Metropolitan Area Transit Commission. There will be no fare increase for rides in District-licensed cabs entirely within the city.

Under the order, a direct five-mile ride from National Airport to the Mayflower Hotel will rise from $5.10 to $5.70, plus a 50-cent airport dispatching fee. A 27 1/2-mile ride from Dulles International Airport to the Mayflower will rise from about $25.35 to about $28.20.

The new rates are $1.70, up from $1.50, for the first mile and 50 cents (up from 45 cents) for each half-mile or fraction thereafter.

Fares for a given trip may vary because of differing routes drivers may use. The fare for each additional passenger in a prearranged group remains at 75 cents. Additional passengers, not members of a group, are charged a full fare.

Fares charged for interstate trips in suburban cabs will continue to be the amounts shown on their meters, plus the 50-cent airport dispatching fee and the 75-cent charge for additional group riders.

Under an interstate compact, the transit commission regulates the cost of taxicab travel only when it crosses state lines. The cost of travel within the District or within either adjacent state is set by local governments. The transit commission uses metered fares set by those local governments for interstate fares, and has adjusted the fares of District cabs, based upon mileages shown on their odometers, to approximately the level of the suburban metered fares.

The most recent interstate taxicab fare increase went into effect in April 1981. The investigation that led to the newest increase was undertaken at the commission's own initiative.