Government Employes Insurance Co. will be able to end by June 30 the arrangement under which other insurance companies have assumed part of Geico's risks to keep the company solvent.

At the company's annual meeting yesterday, Chairman John Byrne said termination of the reinsurance "treaty" as it is called, signals the return to financial independence for Geico.

Forged in 1976 when Geico was in danger of going under, the treaty provided for a group of other companies to reinsure about 25 percent of Geico's business in return for control of $150 million of Geico's assets.

At that time, it was believed Geico would need the backing until 1980 or 1981, Byrne said, but Geico's spectacular recovery has made it possible to terminate the agreement by the middle of this year. Geico took back about one-quarter of the reinsured business last year and has reduced the reinsurance further in recent weeks.

After losing $156 million in 1976, Geico turned in a $58 million profit last year, and Byrne said termination of the treaty woule mean higher profits in the future.

The companies that have handled the reinsured business have been making money on it and those profits will now flow to Geico. In addition, the company will regain control over $115 million in assets that can be invested profitably.

Byrne declined to setimate Geico's profits this year, but told stockholders, "When I think to the future, my outlook is bullish. The word that comes to mind is 'acceleration.'"

He predicted steady growth in premiums, "much better" underwriting income, and a solid future because of the company's investment profits.

Because the company still has more than $100 million in tax losses to offset profits, all of those earnings will show up on the bottom line of the company's financial report. But he said the company will have to strengthen its balance sheet before it can increase its 5 cent-per-share quarterly dividend.

In contrast to past meetings when hundreds of shareholders questioned and cajoled Geico executives, this year's annual meeting was uneventful. A handful of shareholders offered minor suggestions, but there was no criticism of the company now that it is turning around.

With no opposition, shareholders added Dr. Clarence Walton, president of Catholic University, to Geico's board. Two veteran directors, Lorimer Davidson and William Jacobs Jr., did not stand for re-election.

In a series of annual meetings of affiliated companies that followed the Geico session, Byrne was added to the boards of Government Employes Life Insurance Co. and Criterion Insurance Co.

Martin Hart, a Denver investor, was elected to the board of Government Employes Financial Corp.

Gelico President Thomas Hefner said that company had a 2 percent increase in sales of life insurance policies during the first quarter of 1978. It was the first increase in sales since the first quarter of 1976, he noted raising Gelico's total insurance in force to $2.3 billion.

Geico President George Lewin said the first three months of this year procued a 14 percent increase in new business for that auto insurance firm.

The Denver-based finance company operation, Gefco, which produced record profits when other companies had problems, reported progress in two key strategies.

President Ernest Marks said 95 percent of loans now are unsecured personal borrowings compared with 50 percent collateralized loans five years ago. After relying on short-term borrowing fro funds. Gefco last year got long-term financing and re-entered the commercial paper market, lowering its money costs.

Byrne told a questioner that Geico has no plans to make further purchases of stock in the affiliated companies now that a tender offer increasing its holdings in the affiliates has been completed.