Mayor Marion Barry yesterday asked the D.C. Public Service Commission to act quickly and grant city taxi drivers a requested 10.5 percent increase instead of the 10-cent-a-ride rate increase approved June 19.

The increase urged by Barry would raise from $1.20 to $1.35 the cost of a one-zone trip and from $2.40 to $2.65 the cost of a three-zone trip. The 10-cent-a-ride rate boosts already approved, equal to about 3.5 percent, increased the cost of a one-zone trip to $1.30, and that of a three-zone trip to $2.50.

Barry said the higher rate increase is justified by steep increases in the cost of gasoline, purchase and service costs during the past four years, and because suburban cab drivers have recently received large increases.

Montgomery County drivers were granted a 25-cent to $1 surcharge Wednesday. Drivers in Airlington were earlier permitted to begin assessing a 30-cent surcharge.

Edward M.Meyers, special assistant to the mayor for fiscal affairs, said the special request for prompt action was made because the administration is concerned that the rate increase request be decided before the end of the summer.