Maryland National Corp., owner of the State's largest banking firm, yesterday reported a 22 percent increase in operating profits in the first six months of 1981 to a record $20.1 million ($2.64 a share) compared with $15.6 million ($2.17) in the same period last year. Separately, MCI Communications Corp. of Washington reported a sharp increase in profitability for its first fiscal quarter.

Marynat, the parent firm of Maryland National Bank, also posted an increase in second-quarter earnings before securities transactions of $9.6 million ($1.25) a share compared with $8.8 million ($1.23) a year ago.

Net income for the quarter was $9.4 million ($1.23) versus $8.3 million ($1.16), while six-month net income rose to $19.8 million ($2.59) from $14.5 million ($2.02.

Chairman Robert D. H. Harvey attributed the record level of profitability to a sharp increase in interest income, better results from nonbanking subsidiaries and about $1.4 million from redemption of Penn Central securities in the first quarter. Assets totaled $4.4 billion on June 30.

NS&T Bank of Washington said second quarter operating profits rose to $1.37 million ($2.99 a share) from $1.34 million ($2.92) a year earlier. Net income was $1.34 million ($2.93) versus $1.34 million ($2.92).

For the first six months, the D.C. bank reported operating earnings rose 17 percent to $2.5 million ($5.54) from $2.2 million ($4.74). Deposits rose 8.6 percent over the past 12 months to $429 million on June 30. NS&T directors also voted a regular quarterly dividend of $1.20 a share, payable Aug. 1 to stockholders of record July 23.

National Bank of Washington reported a 54 percent increase in second-quarter profits, as profits rose to $794,927 (57 cents a share) compared with last year's second-quarter earnings of $517,767 (37 cents). For the first half of the year, NBW profits declined to $1.56 million from $1.88 million for the same period last year.

MCI Communications earned $10.7 million (19 cents a share) in the first fiscal quarter ended June 30 compared with operating profits a year ago of $2.8 million (2 cents). In the 1980 period, a tax loss credit of $1.2 million increased net income to $4 million (5 cents).