Chesapeake & Potomac Telephone Co. of Maryland said yesterday it would delay its request for a $123 million rate hike for 60 days after the Maryland Public Service Commission "strongly" suggested that the company give all parties involved more time to examine the case.

"We have advised the commission we will accept their suggestion that the company allow an additional 60 days for consideration of the application," a telephone company spokesman said.

The Maryland people's counsel has asked the commission to throw out the rate application on the grounds there would not be enough time to examine financial data submitted by C&P of Maryland. The rate increase is scheduled to go into effect next March, but the company's final 1984 data will not be available until the end of February, the People's Counsel complained.

C&P's acceptance of the 60-day delay means that the rate increase won't become effective until May.

C&P of Maryland has based its rate request, which would raise residential rates by about 25 percent and business rates by about 28 percent, on financial data from the first six months of 1984 and projections for the rest of the year, said Gregory Carmean, an assistant Maryland people's counsel. Regulators typically base decisions on rate requests on a utility's actual revenues and expenses over a one-year period.

The District Public Service Commission is expected to rule in the next two weeks on a similar motion by the D.C. People's Counsel to dismiss a $75.8 million rate hike request from C&P Telephone Co.