Buttressed by an earnings statement showing a substantial increase in profitability, directors of Government Employees Insurance Co. yesterday voted to pay a cash dividend on common stock for the first time since early in 1975.

Directors of a Geico affiliate, Criterion Insurance Co., also voted a cash payout on common stock -the first since mid-1975.

Geico, an automobile insurance firm that was considered close to insolvency 15 months ago, reported third-quarter profits of $18.5 million (96 cents a share) compared with $5.8 million (33 cents) in the same period last year.

For the first nine months of 1977, Geico's profits soared to $41.9 million ($2.11 a share) compared with a loss of $34.3 million in the comparable months during 1976.

Profits for the recent quarter and first nine months were augmented by tax benefits that developed during the period that Geico was suffering losses. These extraordinary credits, included in the profit figures cited above, were $6.8 million for the quarter and $13.8 million in the nine months.

"We continued to grow in financial strength during the third quarter," said chairman John J. Byrne. "Our goal of stabilizing operations has proceeded according to plan."

At the same time. Byrne said Geico still suffers from inadequate profits on underwriting auto policies. For the year to date, Geico had an underwriting loss of more than $6 million, he said.

A new marketing program "is generating thousands of new business inquires each week," he added. This program, designed to halt a decline in Geico's customer base and to add new business, apparently has helped to stabilize the company's number of outstanding policies.

Because of these improvements, Byrne said, a cash dividend will be resumed with an initial quarterly distribution of 3 cents a share on Dec. 30 to stockholders of cecord Dec. 6 Geico's last dividend was 20 cents a share on March 28, 1975.

A regular quarterly dividend of 18.4 cents on cumulative preferred stock also was voted, payable Jan. 1 to stockholders of record Dec. 6.

Directors of Criterion approved a dividend of 15 cents a share, payable Dec. 29 to stockholders of record Dec. 6. An announcement said the decision "signals a resumption" of paying out in cash dividends to shareholders "a moderate portion" of profits.

Earlier this week, Criterion posted a sharp gain in earnings for 1977. The firm's last dividend was a semi-annual payment of 20 cents on June '0, 1975.

Government Employees Life Insurance C.O. (Gelico) directors, at a separate meeting, approved a regular quarterly dividend of 9 cents a share, payable Dec. 29 to stockholders of record Dec. 6.