Government Employees Insurance Co. plans to terminate this year an agreement with competing firms under which the other insurers assumed a share of the local company's risks to help prevent a Geico insolvency.

Based on a sharp turnabout in Geico's financial condition, the agreement on reinsurance has been reduced by a quarter to 19.02 percent of Geico's total business from the initial 25.36 percent late in 1976.Some $33 million of assets have been returned to Geico, the company said in its annual report to stockholders yesterday.

Geico Chairman John J. Byrne also reported that his firm's surplus for the protection of policyholders, a measure of financial soundness, exceeded $178 million at the end of 1977 - "significantly higher than ever before in our history."

And Geico also earned a record $58.6 million for its stockholders ($1.70 a share, assuming an exchange of convertible shares), compared with net losses of $26.3 million in 1976 and $126.5 million in 1975.

As reported earlier, an accompanying proxy statement for the annual meeting on April 12 reveals that former chairman Lorimer A. Davidson and director William K. Jacobs Jr. plan to retire from the Geico board. Davidson has been a director since 1952 and Jacobs, since 1948. Both will continue as consultants to the auto insurance firm.

Nominated to fill one of the board vacancies was Clarence C. Walton, president of Catholic University. Among other developments detailed in the report and proxy statement:

American Financial Corp. of Cincinnati, a financial holding company engaged in insurance and banking, has acquired 912,500 shares of Geico preferred stock or about 11 percent of that class outstanding. Most of the shares were acquired by the end of last March by Great American Insurance Co., an American Financial subsidiary.

According to a Geico spokesman, American Financial has described its Geico stock acquisition as an investment. Geico last year purchased shares in affiliated companies previously owned by the Cincinnati company.

Berkshire Hathaway Inc., a diversified company, continues as the largest single investor in Geico, owning 1.29 million shares of common (7.29 percent) and nearly 2 million shares of preferred (24 percent).

Two class actions filed against Geico and certain officers and others by stockholders, alleging violations of securities laws, have been the subject of "active" settlement negotiations.

An agreement in principle has been approved but the talks are continuing. An amount of money "not material in amount" was set aside in the 1977 accounts to cover any liability involved.

Geico's board of directors has established a new "social responsibility committee," including six members. Arts patron and former company chairman David Lloyd Kreeger heads the committee, which assesses hiring, community and charitable activities.

Byrne said Geico's premium volume last year was $463.6 million, down from $575.4 million the previous year. But Geico's written premiums for the 12 months ended Dec. 31 increased over the previous such period three months earlier for the first gain since mid-1976.

Policies in force also declined throughout 1977, but the rate of reduction was less in each succeeding quarter. The company had 1.27 million auto policies at year's end compared with 1.61 million a year earlier.