Henry G. Cisneros, Democratic mayor of San Antonio and incoming president of the National League of Cities, said today that drastic deficit-cutting measures nearing approval in Washington will devastate city finances throughout the country and could bring the end of "the federal system as we know it."

Similar sentiments were expressed by Cleveland Mayor George V. Voinovich, a Republican and the league's outgoing president, who said today the Gramm-Rudman-Hollings budget plan could mean the end of any significant federal role in domestic policy.

The 38-year-old Cisneros, a leading contender last year for the Democratic vice presidential nomination, reflected a mood as gray and gloomy as the clouds hanging over the Space Needle as 4,000 mayors, council members and city delegates gathered here for the league's annual convention. He said he expected many mayors would lose their jobs once voters began to feel the effects of the Gramm-Rudman-Hollings plan.

Already reeling from the scheduled end of $4.6 billion in annual revenue-sharing payments in 1987, officials said the plan removes any chance of restoring even a portion of revenue sharing and opens the way for President Reagan to seek to cut funds already promised the cities for this fiscal year.

Mark Israel of the National Center for Municipal Development said the impact on the cities he represents "ranges from disastrous to more disastrous."

The Gramm-Rudman-Hollings compromise reached Friday by House and Senate negotiators would reduce the federal budget deficit -- now about $200 billion -- to zero by 1991 through a series of across-the-board spending reductions except for Social Security and some poverty programs. The cuts would be divided evenly among domestic and military spending.

Cisneros said in an interview that the convention will ask Congress to step back from Gramm-Rudman-Hollings and explore tax increases or other ways to balance the budget, but he did not express much hope that this effort would soon succeed.

Cleveland's Voinovich suggested that some members of Congress feel they cannot safely vote for tax increases until voters feel the pain of reduced fire and police protection and road maintenance services.

If the conference report passes both houses of Congress and is signed by the president, Cisneros said, "the next 18 to 20 months could see a dramatic and fundamental change in the workings of the government system we rely upon today."

He said many cities would be forced to seek tax increases to pay for essential services, after five years in which local taxes in many areas have already been raised substantially while federal taxes were cut. He said San Antonio voters recently passed a $100 million bond issue that will raise taxes 14 percent.

Voinovich, he noted, has sought tax increases six times in six years, winning voter approval twice. The Cleveland mayor said today he will have to ask for another increase if the federal cuts go through.

San Antonio, with a vibrant economy, expanding borders and an expanding tax base, has many advantages most U.S. cities do not share, Cisneros acknowledged. In many cases, he said, state laws limit the amount of tax increases cities can seek.

Also, he noted the tax overhaul bill now being considered in the House, although preserving some advantages for residents of high-tax cities, would reduce the tax advantages cities have used to sell bonds to replace worn equipment and service growing populations.

Cisneros said if the congressional cuts go through, much of his tenure as league president will have to focus on helping cities cope with financial catastrophe. "We will have to devise new pragmatic, innovated approaches to survive and hopefully in some instances come up with enough local solutions and self-help initiatives that we can actually prosper."

He said cities would have to share information on encouraging private investment and reorienting local economies to fill the gap.

The comments reflected Cisneros' relentlessly upbeat public image, a part of what has attracted Democratic Party operatives looking for new national leaders. Shortly before the interview, Cisneros sat chuckling as San Antonio reporters, city staff and council members gathered in his hotel suite for breakfast lampooned his speaking style, his calls for "two-fisted progress."

First elected mayor in 1981 and reelected in April for a third term with 73 percent of the vote, Cisceros said he plans to run for reelection again in 1987 and sidestepped a question about national ambitions. He has a master's degree in public administration from Harvard and a doctorate in that field from George Washington University, and he emphasized the challenges of his job as mayor and new league responsibilities.

"I believe in the cities -- it's been my training," he said, "and this gives me an opportunity to work on the things I've said I cared about in every working hour for the last 16 years."