Mayor Marion Barry, whose financial rescue plan for the District of Columbia depends on White House and congressional approval, said yesterday that he will seek a meeting with President-elect Ronald Reagan and will soon consult with prominent Republicans to ask for their cooperation and support for the city.

Despite being caught off base by the Republican landslide in Tuesday's election that swept away a friendly presidential staff and eroded congressional support for the city's proposals, Barry expressed optimism about the next four years.

He said it would be a mistake to assume that Reagan or the new conservative members of Congress will be hostile to the District or unaware of the city's unique sensitivity to federal government policy. "I don't want to write off" the possibility of an increased federal payment to the city or his plans for new borrowing from the Treasury "until I've talked to people in the Reagan administration and to Gov. Reagan," he said.

The mayor, a Democrat, said last month that a Reagan victory would be a "disaster" for the city, but his comments in a discursive interview in his office yesterday indicated that he is prepared to seek an accommodation with the new political reality, rather than fight it.His ties to the Republican right are minimal, but he ticked off the names of several GOP contracts he plans to approach, ranging from Sen. Charles McC. Mathias of Maryland, who is in line to become chairman of the Senate D.C. Appropriations subcommittee, to a former member of Reagan's California cabinet who is trying to organize a "Christian inaugural" for the new president.

In the interview, the mayor also:

Predicted that many months and possibly a year would go by before legalized lottery and daily numbers games are operating in the District. Voters approved the city-run gambling in a referendum Tuesday, but Barry noted that there is no money for "start-up" costs in the current budget and also said that congressional approval of the wagering might be difficult to obtain.

Said he is contemplating an appeal to the suburban lawyers, doctors, architects and other professionals to whom the city owes $41 million in refunds from an illegal tax, to forgo the money as a "contribution" to the city's well-being. The city has promised to pay by April 1, but unless Congress and the White House approve Barry's plan to borrow $215 million from a subsidiary of the U.S. Treasury -- a crucial component of the mayor's overall financial program -- there is no visible source for the refund.

That borrowing plan is part of a long-range program the mayor unveiled in July to pay off a cumulative city deficit estimated at $409 million, balance future budgets and cope with the skyrocketing cost of city worker's pensions. Many components of the plan, such as an increased federal payment, new taxing authority and the new borrowing power, depend on approval in Congress and the White House. Barry had spent months briefing Carter administration officials and key members of the democratic-controlled Congress in a quest for their support and recognizes that the election of Reagan might kick the props out from under the entire program.

Barry indicated that he thinks hard political spadework rather than complaint or recrimination may bring the new powerhouses of government around to his view of urban problems. "I'm concerned about what's going to happen to cities," he said, because the Republican triumph marks "a whole swing to more conservative attitudes about government and government involvement . . . On the other hand, we may be pleasantly surprised. There may be some receptivity to a new approach to saving the cities. I don't know."

With the accession of Sen. Strom Thurmond, a conservative South Carolina Republican, to the chairmanship of the Senate Judiciary Committee, the District's proposed legislation to transfer criminal prosecutions here away from the U.S. attorney to a locally chosen District attorney seems to be in deep jeopardy. But the mayor said he would argue that if the conservatives in the GOP really want to get the federal government out of local and state affairs, this bill is a good place to start.

Among the Republicans the mayor said he knows personally or would soon contact are some household political names here and others who are still unknown. The mayor, who spent his early years in Tennessee, said he "thinks we will have some help" from that state's Sen. Howard Baker, who is probably going to become the Senate majority leader.

Barry said he is on good terms with Sen. Bob Dole because he struck up a social acquaintance with Elizabeth Hanford when she was a Nixon appointee on the Federal Trade Commission and has kept it up since she married Dole in 1975.

Still, Barry admitted he was "struggling" to find Republican contacts. He said, "I know Bob Carter." Carter, the D.C. Republican chairman, is executive assistant to William Casey, Reagan's campaign manager. Barry said he had been promised help by James T. Lynn, who was Nixon's budget director and secretary of Housing and Urban Development and is now president of the Federal City Council, a group of D.C. business and professional leaders who study various problems confronting the Washington area. And Barry said he is tryng to arrange a meeting with James Johnson.

Johnson, who is black, has been a Reagan supporter associated with conservative causes for many years. He was Reagan's state director of Veterans Affairs, and later served in the Nixon administration as a Civil Service commissioner and as assistant secretary of the Navy. In 1972, Johnson was identified in a Washington Post story as the subject of a congressional inquiry into charges that he used his position in the government to help a former business associate sell insurance to government workers. He was never formally accused of any wrongdoing.

"I was going to call him last week," Barry said, "because he is trying to put together what he calls a Christian inaugural . . .. He wants to have choirs and singing and sodas and popcorn and no alcohol."

"I suspect that the Reagan administration, in its approach to Washington, D.C., will be similar to the Carter administration, where the people coming in had no real idea of the uniqueness of the District," Barry said hopefully. i

"That happened in 1976 when the people from Georgia, Jack Watson, Ham Jordan, all who came to the Carter White House, they didn't understand the uniqueness. When I first met with Bert Lance, the budget director at that time, we went through the whole federal payment business and he was just amazed that this is the way it works," Barry said. The federal payment is the annual grant Congress makes to the city in lieu of real estate taxes on federal property.

On the professionals' tax -- which the mayor is planning to ask Congress to reinstate next year -- Barry said he hoped to hold the refunds to less than the $41-million settlement approved by a D.C. Superior Court judge last month. Because most of those who paid it deducted it from their federal income tax, he said they might decide now not to claim refunds that would then increase their federal tax liability. He said he was contemplating a personal letter to all those eligible for refunds, suggesting that they forgo them since the professionals have already paid the tax and their point of view has prevailed in the legal proceedings.