The National Urban Coalition, forged out of the urban riots of the 1960s, celebrated its 15th anniversary on a grim note yesterday with the release of an ominous state-of-the-cities report.

"There is no doubt in my mind that the cities are in much worse shape now than they were in 1967, with unemployment rampant . . .and with most cities having reached the limit to how much they can raise through local taxes," said M. Carl Holman, president of the coalition. "We are in a very desperate situation."

The report was replete with attacks on President Reagan's budget cuts and warnings about the prospects for a return to the long, hot summers of 15 years ago.

"The whole notion of burning down your own neighborhood is passe," wrote Leon Finney, executive director of the Woodlawn Organization, a coalition affiliate in Chicago, in one section of the report. "So we're likely to see organized guerrilla warfare, striking out to downtowns and other affluent city areas."

The report said city governments, which are watching their tax bases erode, and local nonprofit and religious groups lack the resources to pick up the slack from proposed domestic budget cuts of $140 billion over the next three years.

The report did not outline any specific legislative agenda for addressing the ills of the cities. Instead, it called for increased political activism by urban dwellers.

Holman gave a qualified endorsement to the administration's one new initiative for inner cities, the Urban Enterprise Zone concept, but made it clear he did not consider the program adequate to the problems.