Geico Corp., parent company of Government Employees Insurance Co., yesterday announced a tender offer for up to 700,000 shares of its own stock at $60 per share.

The offer, which will begin in about a week, is set to expire two weeks later. Geico stock closed yesterday at $56 1/2 a share, up $2.75.

The buyback plan is linked to a private agreement between the Washington corporation and its major shareholder, Berkshire Hathaway, which will sell up to 350,000 of its Geico shares on the basis of one share for every two shares tendered by other owners. In that way the Omaha-based holding company, headed by financier Warren E. Buffett, would maintain its current one-third interest in Geico.

Berkshire Hathaway owns 7.2 million shares of Geico. The bulk was purchased in 1976 when the stock was selling between $4 and $7. Buffett's profit would be about $20 million if his company sold its entire allotment of shares.

Reached at his office, Buffett declined to comment on the tender offer. However, Louis Simpson, Geico's senior vice president and chief investment officer, said Geico had initiated the offer, which could cost Geico as much as $63 million. The parent company plans to use surplus funds it does not need for its insurance operations.

In the past, Geico has purchased its own stock on the open market. But this is the first time since 1978 it has launched a tender offer for it. The tender is a quicker, cheaper and surer method of protecting the current ratio of holdings, according to Simpson.

The proposed purchase, which will be handled by Salomon Brothers, does not indicate a change in ownership or objectives, according to analysts. It will benefit shareholders by increasing Geico's return on equity and future earnings.