When the National Urban Coalition was founded nearly 15 years ago, many of the country's urban residents had expressed their frustration and anger through rioting. Yesterday many of the guiding lights behind the coalition were saying that the hardship and resentments caused by the current recession have renewed the possibility of violence.

"There's no doubt in my mind the cities are in a worse state than in 1967," said M. Carl Holman, the coalition's president. "I have a feeling we are facing an explosive situation," said the Rev. Theodore Hesburgh, president of the University of Notre Dame. "There's no way it can't be, with 50 percent unemployment among minority youth. I don't want to make self-fulfilling prophecies, but if kids aren't working, they will be on the streets."

The coalition members and their honorees at the annual "Salute to the Cities" dinner at the Washington Hilton last night spent a somber day assessing the impact of the economy and federal policies on the cities and expressing nervousness about discussing the possibilities of riots during the summer. "It starts young people thinking maybe this is the only way to do it," said William Donald Schaefer, the mayor of Baltimore. "What makes me unhappy about it is that it says this country only cares about these people . . . if they are going to be destructive," said Holman.

After loud complaints about the length of last year's dinner, which lasted until midnight, the coalition reorganized the program, giving 18 awards before the filet mignon meal. The experiment went smoothly though the baskets of bread and the raw vegetable platters were demolished during the 1 1/2-hour ceremony.

Most of the awards went to those who had demonstrated their commitment long before the Reagan private-sector initiative, such as Avon Products Inc., and who had built up their neighborhoods long before the New Federalism, such as Washington's Thelma Rutherford, an activist now with the Gray Panthers. Robert McMillan, a vice president of Avon, oversees a $2 million foundation that last year, for example, awarded a scholarship to a Miami youth who lost a leg in that city's riots. "I gave a speech dealing with the New Reality, stressing improving volunteerism, doing in-house printing, refocusing grants. Our daily mail for requests is now up 100 percent over a year ago," said McMillan. Other award recipients included Schaefer; Hesburgh; Robert Pippitt, the senior vice president of Xerox; William Lucy, the international secretary-treasurer of the American Federation of State, County and Municipal Employees; attorney Vernon Jordan; Frank T. Judge Jr. of Ford Motor Co. and Norman E. Auerback of Coopers and Lybrand.

Quietly, said Washington Mayor Marion Barry, he has been pulling together a strategy for the summer. "Besides jobs from private and public sector, we are going to get feedback from the neighborhood and have groups of 50 or so people on the streets to be our eyes and ears," said Barry, who stopped at one table and received a champagne toast from a group of reelection supporters, who included Ronald Brown, an attorney and Sen. Edward Kennedy's former assistant campaign manager; Alexis Herman, former director of the Labor Department's Womens Bureau, and former assistant secretary of labor Ernest Green.