Claiming they are being squeezed between rising costs and increasing Metro subway competition, District of Columbia taxicab drivers have asked city officials to approve a stopgap increase in fares without waiting for formal public hearings.

As a result of cab industry requests, the D.C. Public Service Commission is expected soon to consider an immediate 10 percent rise, to be followed by consideration of a larger permanent increase.

A 10 percent interim increase would push the present one-zone cab fare from $1.10 to at least $1.20 and a two-zone fare from $1.55 to at least $1.70, with the cost of longer rides risdes rising proportionately.

Initially, at least, there would be no change in the zone system or zone boundaries that are used to reckon fares. Some drivers have asked the PSC to consider such changes as part of any permanent fare increase.

"Cab service in the District of Columbia has deteriorated tremendously in the past few months," Daniel Smith, attorney for several cab companies, told a recent PSC session on the fare proposals. "Certainly Metro has afforded us much competition, taken away a lot of the ridership... and will continue to do so."

Smith said the number of cabs on city streets, once 8,000, has dwindled to about 6,800 as a result of the financial squeeze on cabbies. In Washington, most cabs are owned by their drivers. Other drivers rent vehicles from cab companies.

Some cab spokesmen contended that the expense of operating taxicabs has rise more than 40 percent since the last fare increase was granted three years ago. That increase followed hearings and deliberations that stretched over two years.

The pending formal petition that asked the PSC to consider higher cab fares -- but not proposing any specific amount -- was filed Sept. 15 by one organization of cab drivers, the Alliance of Taxicab Businessmen.

On Nov. 15, the same day on which the PSC conducted a preliminary exploration of the alliance's request, another organization called the Taxicab Industry Group asked the PSC to conduct hearings on a 20 percent increase in fares. It asked that 10 percent be granted immediately.

The industry group also asked that some form of automatic escalator be devised for future fare increases.

Following the Nov. 15 session, both cab organizations have said they would support a 20 percent interim increase.

Elizabeth Noel, who is responsible for representing the public interest before the PSC as its deputy people's counsel, objected to the 20 percent figure. She said it was far out of line with President Carter's anti-inflation deadline that puts a 7 percent cap on most price rises.

Noel said yesterday that the commission's legal staff is preparing a statement of facts on a potential 10 percent interim increase, to be presented soon to the three PSC members for a decision.

Mello Cottone, a lawyer for the taxicab alliance, said the three-year lag in granting cab fare increases was a disgrace."You can have a hearing in an hour," Cottone said, adding later that the PSC continues "to apply the legalistic and administrative procedures" that apply to setting rates for such large utilities as Pepco.