Prime Minister Maurice Bishop of Grenada, a tiny Caribbean island that President Reagan contends is building an airport for Cuban military use, said yesterday that he has given the United States "concrete assurances ad nauseum" that the airport is strictly for commercial purposes and will not be available to Cuban or Soviet military flights.

Bishop, whose revolutionary government has been sharply attacked by the Reagan administration because of its ties to Cuba, said at a news conference here and in a meeting with reporters and editors of The Washington Post that he wants to open a dialogue to improve relations with the United States.

He said the administration has not responded to his request for a meeting with Reagan during his private visit here this week. The administration has refused to exchange ambassadors with Grenada and has maintained only the most minimal, low-level contacts with Bishop's government.

In two recent speeches on Latin America, Reagan has singled out Grenada's construction, with Cuban help, of a new airport capable of handling large jets as an example of communist penetration of the hemisphere.

On March 10, Reagan ridiculed the argument of a "so-called expert that we shouldn't worry about Cuban President Fidel Castro's control over the island of Grenada--their only important product is nutmeg."

He added, "It isn't nutmeg that's at stake in the Caribbean and Central America. It is the United States' national security."

Then, in his so-called "Star Wars" speech March 23, the president showed an aerial photograph he described as the Grenada airfield construction, and said, "The Soviet-Cuban militarization of Grenada can only be seen as power projection into the region . . . . "

In response, Bishop said Reagan did not need to send a "spy plane" to obtain photos of the field, adding that it is "the No. 1 attraction" for thousands of U.S. tourists annually. They can roam the entire construction area and "take all the pictures they want."

Bishop said studies dating to the 1950s, long before his government took power in 1979, have found that an improved, international airport is necessary for expansion of Grenada's tourist industry and export of sugar and fruit products. Construction has been aided by Britain and the European Economic Community, and dredging was done by a Miami firm, he noted.

Bishop characterized as "totally inaccurate" U.S. charges that the airport is to serve as a refueling and staging area for Cuban troops going to Angola. Bishop said he ruled out military use of the facility in numerous public statements and in two unanswered letters to Reagan.

Responding to questions about whether he intends to turn Grenada into a Marxist society on the Cuban model, Bishop acknowledged that his government regards itself as "revolutionary," sympathetic to other grass-roots revolutionary movements and "truly nonaligned."

He said he could not understand why Grenada's good relations with Cuba should be such a source of concern here since the United States is on good terms with Mexico and Panama, both of which "have a higher level of relations" with Cuba.

He also said that at a Saturday dinner of Trans-Africa, a private U.S. organization that helped arrange his visit, he will reply to critics who charge that he is a dictator by announcing a plan to move toward elections.