Three of Maryland's largest banking corporations yesterday reported continued increases in profitability during the fourth quarter of 1979 and substantial increases for the full year.

Maryland National Corp., the largest banking business in the state and owner of Maryland National Bank, reported operating profits for the year of $25.9 million ($3.63 a share) compared with $21.6 million ($3.03) in 1978.

The operating performance does not reflect gains or losses from selling securities. Marynat had losses on such transactions for both years which reduced net income from $24.8 million ($3.49) to $21.1 million ($2.96).

In the fourth quarter, operating profits rose to $5.9 million (82 cents) from $5.4 million (77 cents).

Chairman Robert D. H. Harvey said the record earnings of 1979 -- up 20 percent in the year -- reflected sustained gains in net interest income and a strong performance by non-bank subsidiaries, which collectively reported the highest annual earnings in history ($2.2 million, or twice the 1978 level).

Average assets during the year rose to $3.35 billion from $3 billion as loan volume increased to $2 billion from $1.9 billion. Marynat opened two branches in the state last year bringing its total number of offices to 148 in Maryland. The firm also opened a representative office in San Paulo, Brazil, and started a new subsidiary, Maryland National Mortgage Corp.

Return on average equity in Maryland rose to 13.1 percent in 1979 from 11.9 percent in 1978.

First Maryland Bancorp, owner of First National Bank of Maryland, said operating profits rose last year to $18.9 million ($5.05 a share) from $15.3 million ($4.12) in 1978. Fourth-quarter profits increased to $4.7 million ($1.26 a share) from $4.1 million ($1.11).

Mercantile Bankshares Corp. said operating efforts were $12.9 million ($4.10 a share) in 1979 compared with $10.8 million ($3.31) in 1978. Fourth-quarter earnings rose to $3.26 million ($1.06) from $2.6 million (78 cents).