Commercial bank deposits in metropolitan Washington increased substantially in the fourth quarter of 1978, helping to advance full year totals by some 13 percent to a record $12.15 billion compared with $10.74 billion in 1977.

According to a Washington Post survey, the 1978 growth was strongest for institutions based in the District, where deposits soared 17 percent to $5.85 billion. In the Maryland suburbs and Northern Virginia, the rate of growth was about 9 percent.

Overall, suburban deposit totals still exceed those in the city by $450 million ($6.3 billion vs. $5.85 billion) but the gap is narrowing. A year ago, suburban totals were ahead by $800 million. According to area bankers, the new gains by D.C. institutions reflect the city's construction boom, growing trade association and international business and more aggressive commercial and retail (consumer) marketing efforts.

Summaries of D.C. and Maryland deposits were published earlier. In Northern Virginia, deposits on Dec. 31 were $3.05 billion compared with $2.8 billion a year earlier and $2.97 billion last Sept. 30.

The largest gain in the area's Virginia banks was reported by First Virginia -- up $77 million to $531 million, resuming a lead over United Virginia Bank/National. The new First American Bank (representing a merger of three Financial General Bankshares units, Clarendon Bank, Arlington Trust and Alexandria National) is now largest in Northern Virginia, with deposits of $643 million, up $9 million from combined deposits a year earlier.

In the summary of Maryland deposits, published Jan. 21. yearend deposits of the Prince George's State Bank were inadvertently omitted. The new minority bank had Dec. 31 deposits of $1,721,419.