Marriott Corp. made an unsolicited offer yesterday to acquire Host International Inc., the nation's largest operator of airline-terminal food, beverage and merchandise facilities.

The Bethesda-based hotel, restaurant and airline-catering company offered $29 each for Host's 4.8 million outstanding common shares. Host Chairman and President Howard E. Varner said directors will review the cash tender offer and merger proposal at a special meeting on Monday.

Marriott's offer tops an earlier one accepted by Host. The company had announced an agreement in principle on Nov. 1 to merge with DFS Group Ltd. of Hong Kong at a price of $24.25 a share of Host common stock. DFS is a privately owned company that sells duty-free merchandise primarily in the Pacific and West Coast cities. It had sales in excess of $500 million in 1980.

Host and Marriott compete for contracts to operate airport-terminal restaurants and shops, and to provide airlines with in-flight food service.

Based in Santa Monica, Calif., Host is a food service and retailing company that operates restaurants, bars and shops at 25 airports in the United States, including food and merchandise facilities at Baltimore/Washington International Airport. Host also provides contract food service to airlines at five or six airports, a spokesman for the company said.

Host also owns 52 specialty restaurants in California and the East Coast, including 16 restaurants in the Washington area and five eastern states that it acquired from Marriott in 1979.

Marriott is said to be the largest domestic provider of in-flight catering services to the airlines. As of last year, it also operated 16 airport terminal restaurants and shops, a Marriott spokesman said.

Host closed on the New York Stock Exchange yesterday at $22 a share, up 25 cents for the day on a volume of 48,200 shares. The previous day, Host trading soared to a volume of 114,000 shares and the stock jumped $1.13 after being unchanged in the previous two sessions when volume was in a range of 20,000 to 40,000 shares.

Marriott said yesterday its offer to Host is conditioned upon its approval by Host's board of directors and their favorable recommendation to Host shareholders. Marriott asked that Host respond to its offer by next Tuesday.

Host had profits of $14 million on sales of $357 million in 1980. In the first nine months of this year, its earnings fell to 47 cents a share from $1.20 in the same period of 1980. A spokesman said the company wasn't as profitable this year because a duty-free-shop contract in Honolulu has been terminated.

Marriott, which reported profits of $72 million last year on sales of $1.7 billion, also has been talking to Gino's Inc., a fast-food chain with 469 stores, about a possible acquisition.