In a ceremony subdued by the siege only three blocks away, President Carter yesterday welcomed British Prime Minister James Callaghan as the leader of "our closest allies and friends." After the formalities the two immediately began talks on economic problems, Rhodesia and human rights.

The traditional 19-gun salute for a head of government by 105 mm howitzers was eliminated from the South lawn ceremony at the request of District of Columbia police. U.S. chief of protocol Evan Dobelle said there was concern that artillery "might be misunderstood" by those involved in "the current problem," his diplomatic phrase for the hostage situation at the District Building nearby. Callaghan's staff "understood completely," Dobelle said.

Making his remarks from note - rather than from memory as in the case of his controversial statement on Israel's borders in his welcome Monday for Israeli Prime Minister Yitzhak Rabin - Carter spoke of the "special relationship" which the United States enjoys with its "mother country." He promised close future cooperation in both security and economic areas.

Callaghan, who is currently president of the European Economic Community, called for "a close partnership and a strengthening of relations" between the United States and Europe. Reflecting Britain's current economic troubles and its request for stronger economic stimulaton measures on the part of the United States, Germany and Japan, Callaghan also declared pointedly, "No one group of nations and no one nation can survive permanent as an island of the world is in recession."

The initial Carter-Callaghan talks at the White House did not touch on the subject of the Concorde supersonic airliner, the French-British plane which is seeking landing rights in New York City. "This was not an issue to start off with," Callaghan later told reporters. Presidential press secretary Jody Powell said he is certain the subject will be discussed before the two-day round of meetings is over.

Callaghan said he had intended to bring up the "special relaionship" between the countries after a few hours of talks with Carter, describing him as shy about doing so initially. Thus he was delighted with Carter's welcome and, according to the British leader, subsequent mentions of the "special relationship" in their private conversations.

Powell went out of his way to emphasize the continuing need for "close cooperation" between the United States and Britain on the movement toward majority rule in Rhodesia. This appeared to be an effort to ease British concern and embarrasement over Monday's remark by Andrew Young, U.S. ambassador to the United Nations, that "no one has any confidence in the British" as guarantors of peace in Rhodesia.

According to Powell, most of the discussion yesterday dealth with international economic matters. He said the two leaders discussed "the dangers of protectionism, which becomes particularly acute in times of recession."

Powell said there was also talk about the forthcoming Belgade conference of nations which signed the Helsinki agreement on human rights and European security. Carter and Callaghan are working on "ways to see that this conference will be productive," he said. He gave no details.