Quality Inns International Inc., which last month introduced a chain of economy hotels called McSleep Inn, has fired the first legal shot at McDonald's in a battle over the McSleep name.

Quality, a lodging company based in Silver Spring, filed suit against McDonald's in U.S. District Court in Maryland asking the court to declare that McSleep does not infringe on the fast-food chain's trademarks. The suit also asks the court to order McDonald's to stop what Quality calls threatening and harassing behavior.

"We take strong exception to McDonald's continuous threats and harassment regarding the McSleep Inn name," said Gerald W. Petitt, vice president and chief operating officer of Quality International, which is a subsidiary of Manor Care Inc.

McDonald's has responded to the suit by saying that the use of McSleep infringes on its trademark and that the public is likely to believe the lodging chain is associated with the restaurants.

In addition, in 1985 McDonald's started using the name McStop for a travel plaza in Lakeville, Minn. The company has plans to develop similar facilities, which include a McDonald's restaurant, a gasoline station and a motel, said Stephanie Skurdy, a McDonald's spokeswoman.

"It could be the basis for a whole new system," said Skurdy.

When Quality introduced the McSleep chain, an economy line featuring rooms for $20 to $29 a night, McDonald's immediately took exception to the name.

"Your use of these marks will not be tolerated by McDonald's Corp.," said a letter addressed to Quality by a McDonald's attorney.

"We must insist that you immediately discontinue using the Mc prefix. ... Should we fail to receive your prompt assurances of discontinuance, we will immediately refer this to outside counsel for handling," Horwitz added.

McDonald's has challenged the use of the Mc prefix for company names in the past, particularly when associated with food servies. In a case in U.S. District Court in New York, McDonald's successfully sued the owner of a McBagel shop, who had to stop using the name.

Quality officials contend that, because their economy line offers no food or restaurant service, there should be no conflict with the food-service business.

The company expects to open about 200 McSleeps by 1991. It has not sold any franchises because it is going through state and federal disclosure requirements, Petitt said.

More than 100 individuals or firms have expessed interest in the franchises, he said.