A picture caption in Sunday's editions erroneously described Tulsa Mayor James Inhofe as being opposed to President Reagan's proposal for consolidating federal categorical aid programs into block grants. Inhofe, in fact, is a strong supporter of those proposed changes.

The U.S. Conference of Mayors opened its annual meeting here today with a sharp partisan clash over President Reagan's efforts to trim domestic spending and give the states added control over federal aid to urban areas.

Gary, Ind., Mayor Richard G. Hatcher, the conference president, told an opening news conference that the Reagan program amounted to "a cavalier abandonment of the cities." But his predecessor as conference president, Peoria, Ill., Mayor Richard E. Carver, said that the President's efforts to revive the economy with budget and tax cuts offered "the best hope" for every city.

The clash between Hatcher, a vice chairman of the Democratic National Committee, and Carver, the head of the Republican Mayors' Caucus, was echoed in committee meetings through the day. Carver won preliminary approval of a resolution supporting broad tax cuts, but was shot down in efforts to put the conference on record as supporting the administration's reductions in urban spending and its efforts to shift many federal categorical aid programs to block grants controlled by the states.

Instead, the conference committee on economic policy approved a resolution by Milwaukee Mayor Henry W. Maier, a Democrat, who argued that "social defense" of domestic programs be given equal weight with "national defense" in setting budget priorities.

All the policy statements will be considered again Sunday in the resolutions committee and then voted on by the mayors at their closing session Wednesday.

Maier, whose 21 years in Milwaukee City Hall make him the senior mayor, was also the most outspoken in his criticism of the spending cuts proposed by Reagan and approved by Congress in its first budget resolution.

"There is going to be blood in the streets as a result of this budget," he shouted in a fist-pounding speech, "either in rising crime rates of in direct riots. After building expectations since 1967, to turn around and destroy those expectations -- it's very, very dangerous."

As the mayors began debating the sweeping changes in domestic programs Reagan has launched, many of their best-known and most influential members were missing. The mayors of New York, Chicago, Los Angeles, Boston, Detroit and San Francisco -- all Democrats -- were at home, some of them because of fiscal crises and some because of their feeling that efforts to reverse the Washington cutbacks are futile.

There was a notably bitter and partisan tone to many of the comments, unusual in a group that subordinated partisanship in its lobbying for increased federal aid during the 1960s and 1970s.

The change reflected the growing tension between some of the mayors and the White House since Reagan took office. Hatcher complained at the news conference that he was the victim of "purposeful execution" when Reagan entertained 50 other mayors in five White House meetings between June 1 and Friday.

But Brian Tierney, the local government liaison for the Republican National Committee, said the White House had chosen not to deal with Hatcher because, "when you see someone like him up there arguing, you have to wonder whether or not he has his hat on as vice chairman of the DNC."

Reagan and Vice President Bush declined invitations to address the conference, leaving that job to Housing and Urban Development Secretary Samuel R. Pierce Jr. and Rich Williamson, the president's assistant for intergovernmental relations.

Carver, serving as the main administration spokesman until their arrival, argued that "a viable private economy is the key factor for the survival of every city."

But the Peoria mayor had a hard time selling his approach in the conference committees. His resolution endorsing tax cuts of unspecified size and duration cleared its first hurdle, but the operative clauses were knocked out of his resolutions that would have put the organization officially behind Reagan's budget and block-grant proposal.

The block-grant plan is perhaps the most controversial part of the administration program for most mayors. Carver himself, in a preliminary resolution that he withdrew today after meeting with White House officials, said that "state governments have not historically demonstrated sensitivity top urban areas. . . ."

Many of the mayors simply do not trust their state governments to pass on funds to urban areas if the federal mandates are removed. As Hatcher said, "If the states decide they want to spend the money on a hot lunch for children, they can. If they want to spend it on a golf course, they can."