The National Conference of Black Mayors opened a three-day conference here yesterday, and promptly voiced opposition to federal and state budget cuts involving aid to the poor, unemployed and elderly as a means of fighting inflation.

"We find ourselves confronted with an administration and a Congress with a disease of budget cutting," said Richard Hatcher, president of the conference of about 194 black mayors.Hatcher is mayor of Gary, Ind.

"Food stamp programs and jobs are being cut back in the name of inflation," he said.

The theme of the convention, "Voting: A Key to Political and Economic Viability," addresses what Hatcher said was a need for black mayors and their constituents to become involved in politics, especially during a presidential election year, in order to have an influence on state and federal policies that will affect their cities and special problems.

While they were critical of President Carter's proposals to fight inflation by cutting federal spending in certain areas, several mayors, including D.C. Mayor Marion Barry, who was sporting a Carter-Mondale button, said they would be supporting the president.

Hatcher said the conference was nonpartisan and would not endorse any candidate.

"There aren't any candidates who agree with me or with Barry on every issue," Hatcher said. "What we've got to do is look on those candidates in a relative sense. It would be a mistake for black mayors not to endorse someone and to try to have an impact on the issues and in the campaigns."

The president entertained many of the mayors yesterday afternoon at a White House reception.

Administration spokesmen for areas such as housing transportation, health, education, welfare and economic development will be available and will attend some conference workshops this weekend, a conference spokesman said.

The conference was established in 1974 and originally was called the Southern Conference of Black Mayors because most of its members were from the South. It concentrated primarily on providing resources and information to newly elected black mayors, said Michelle D. Kourouma, executive director of the conference.

"There is a tremendous information gap between black mayors in small communities and state and federal governments," she said. "Black mayors from small towns have two strikes against them -- being black and being from a small town."

Most of the mayors in the conference are from towns with populations of 10,000 or less. But together, they have a constituency of 20 million people, larger than that of the congressional Black Caucus, a group of black members of Congress, Kourouma said.

Hatcher said the conference's priority topics include unemployment, voter registration and increased participation, ratification of the D.C. Voting Rights Amendment, energy and alternative fuels, utility rates and concern over Zimbabwe.

"For me, the best thing to come out of these conferences is the information and insight on how to get federal monies," said Vaughn E. Hairston, mayor of Urbancrest, Ohio, population 1,000.

"In 1976, after coming to the conference, I got information to get federal monies for a $1.5 million community center for my city, with an Olympic sized swimming pool, a game room and a senior citizens activity area."