Government Employees Insurance Co. yesterday reported earnings for the first half of the year increased to $41.5 million ($2.09 per share) from $23.4 million ($1.17) a year ago.

Geico Chairman John J. Byrne, however, cautioned that premium revenues are still declining and sales to new customers remain "disappointing.

Geico's earnings include $3.6 million from the company's share of its afiliates - Criterion Insurance Co., Government Employees Life Insurance Co., and Government Employes Financial Corp.

Included in the reported earnings are tax loss carryforward credits of $16.7 million (94 cents per share) this year and $7.1 million (40 cents) in the first half of 1976. The tax credits remain from the virtual collapse of Geico three years ago.

Saying the current first half results reflect "steady growth in profits and in capital," Byrne noted Geico now has built its surplus to protect policy-holders up to $189 million.

Termination June 30 of the treaty under which other companies underwrote Geico's policies - and took the profits - means "the final chapters of Geico's return to financial strength are complete," Byrne said.

For the second quarter Geico earned $20.9 million ($1.05 per share), compared with $14 million (71 cents) a year ago.