A worldwide insurance organization, Skandia Insurance Co. Ltd., has boosted its stake in Bethesda-based Avemco Corp. to 205,000 shares, or 8.2 percent, Avemco officials said last week.

Skandia, with headquarters in Stockholm, also has filed a request with the Maryland insurance commissioner for a determination that Skandia would not have controlling interest in Avemco if Skandia raised its holdings to 15 percent.

The request was filed in compliance with the Maryland Insurance Acquisition Disclosure and Control Act. According to Avemco officials, Skandia said it would not buy more than 9.9 percent of Avemco's outstanding shares unless the insurance commissioner affirms Skandia's relative holdings.

Avemco, traded on the American Stock Exchange, is a national aviation insurance, financial services and product marketing firm.

Skandia began acquiring Avemco stock early in March, saying then that it was interested in investment only, not a takeover. On March 26, Skandia's holdings were reported at 6.7 percent of Avemco's outstanding shares.

Avemco officials said last week that Skandia repeated in its request to the insurance commissioner that it was a passive investor with no plans for requesting representation on Avemco's board or changing its management.

William P. Condon, Avemco board chairman, said that his company is "considering what response it may make" to Skandia's actions.

The other major shareholder in Avemco is Geico Corp., which owns 22 1/2 percent of Avemco's voting shares. Geico is barred from obtaining a greater stake in Avemco until July 31, 1984, under a "standstill agreement," which allows Geico to put two directors on Avemco's board.