Maryland National Corp., holding company for the state's largest bank, reported yesterday a modest 7 percent increase in third-quarter profits.

Not counting gains or losses from selling securities, Marynat earned $5.4 million (76 cents a share) compared with $5 million (71 cents) in the same period last year.

Although the third-quarter increase lagged behind profit gains reported this week by other large banking firms, Marynat's nine-month earnings were stronger: $16.1 million ($2.26 a share), up 17 percent from $13.7 million ($1.93) in the 1977 period.

Chairman Robert D. Harvey said the nine-month gain reflected improvement in interest income and a stronger performance by non-banking subsidiaries.

Total assets of Marynat were a record $3 billion on Sept. 30 while deposits at Maryland National Bank averaged $2.1 billion in the first nine months compared with $2.09 billion a year earlier. Loan volume increased to an averaged $1.9 billion from $1.7 billion.

During the recent quarter, Marynat opened its 14th office in Montgomery County in Potomac and ow has 146 offices statewide. The bank also introduced a debit card system and opened a foreign cooperations center in Silver Spring to serve international markets from the washington suburbs.

In addition to the bank, Marynat owns a Towston leasing firm, MN Mortgage Corp. in Florida, an industrial finance subsidiary, Redwood Capital Management, Old Line Realty (joint venture), Maryland National Realty Investors, and Homeowners Loan Corp.

National Bank of Washington, the third-largest D.C. bank firm, reported a 24 percent increase in third-quarter operating profits to $1.57 million ($1.42 a share) compared with $1.26 million ($1.15) a year ago. After securities transactions, net income was $1.3 million ($1.21) vs. $1.27 million ($1.15).

For the nine months, NBW earned $4.5 million ($4.10) from operations compared with $3.2 million ($2.96) in the 1977 period. Net income was $4.3 million ($3.89) vs. $3.4 million ($3.08).

Deposits of the bank, a majority interest of which is owned by the United Mine Workers union, rose 7 percent from last year to $639 million on Sept. 30. Loan volume increased 7 percent to $455 million and total assets were $816 million, up 15 percent.

Manor Care Inc. a Silver Spring nursing center company, recorded earnings in the first quarter ended Aug. 631 or $395,000 (23 cents a share), up sharply from $158,000 (9 cents) a year earlier.

Revenues rose to $11 million from $8.4 million and Manor Care said the recent quarter included $219,999 of profits from its equity investment in Hillhaven Corp., a subject of a takeover bid.

Adams Express Co., a Baltimore investment fund, reported a net asset value of $228 million ($15.19 a share) on Sept. 30 compared with $208 million ($14.28) a year earlier. Third-quarter stock purches by Adams included AMP Inc. (35,000 shares), First United Bancorp. (30,000) and Wisconsin Public Service (78,800). The fund sold 200,000 shares of A.H. Robins.