President Carter closed the door yesterday on Prime Minister Ian Smith's request for a White House meeting where Smith hoped to argue his case for U.S. support of his transitional government in Rhodesia.

"There is no reason for me to meet with him." Carter told a news conference. He noted that Smith and Secretary of State Cyrus R. Vance conferred for two hours Monday in an unsuccessful attempt to agree on a means of bringing about democratic, black majority rule in Rhodesia.

Although Vance said he was willing to meet with Smith again, that possibility appears to have been precluded by the secretary's impending departure Friday for South Africa. Smith then raised the question of a meeting with Carter.

However, when the president was asked about the request, he carefully maintained the coolness that his administration has displayed toward Smith since his arrival Saturday on a private visit.

Ever since Rhodesia's 1965 break with Britain, the United States officially has regarded Smith's white-minority-controlled government as illegal. Smith obtained a U.S. visa only after a furious controversy about whether the Carter administration was trying to suppress his opinions from being heard here.

Issurance of the visa caused the U.N. Security Council to rebuke the United States yesterday for admitting Smith in defiance of U.N. sanctions against Rhodesia. The vote was 11 to 0, with the United States, Britain, Canada and West Germany abstaining.

In rejecting Smith's bid for a meeting, Carter reiterated the U.S. position that the best way to resolve Rhodesia's internal strife lies in a peace conference between Smith's government and leaders of the black nationalist Patriotic Front guerrillas fighting against him.

"We're trying to end the bloodshed in Rhodesia," Carter said. "We're trying to work out a method whereby free and democratic elections can be held in Rhodesia."

Smith has been trying to implement his own so-called "internal settlement" plan for black majority rule, without the participation of the Patriotic Front.

During his U.S. visit, he has asserted repeatedly that his plan meets the requirements of an agreement he made in 1976 with then Secretary of State Henry A. Kissinger. By refusing to support him now, he charges, the United States and Britain have failed to carry our their part of the agreement.

Asked about that assertion yesterday, Carter said he was "not familiar" with any written "executive agreement" between Smith and Kissinger. Smith has contended he has Kissinger's assurances of support "in writing."

That's a reference to a message sent by Kissinger to Smith two years ago after Kissinger made a shuttle-diplomacy trip through southern Africa in an attempt to get the contesting Rhodesian factions to agree on a plan for majority rule.

The text of the message was never made public, although Smith has said it promised him U.S. support if he accepted Kissinger's plan. Kissinger subsequently denied giving such assurances, and the plan then became embroiled in still unresolved controversies about the abiguities of what Kissinger actually told the different parties to the dispute.

Although Kissinger's mission did lead to a conference under British auspices in Geneva, the negotiations collapsed after the Patriotic Front and some of Rhodesia's black African neighbors refused to accept the Kissinger plan.

The United States since has contended that the plan required approval from these so-called "front-line states" and the Patriotic Front before it could be implemented.

U.S. officials say it was the failure of the Geneva conference to achieve this universal approval for the Kissinger plan that led to the current Anglo-American proposal for a peace conference of all parties to work out a power-sharing agreement paving the way for majority-rule elections.