Vice President Mondale received blunt warnings from British leaders today on the problems of Rhodesia and the international economy.

The touring Vice President arrived in London after a private audience earlier today with Pope Paul VI, who told him that the Carter administration's drive to curb nuclear weapons is "of immense service to the world."

In rainy London, the personal cordiality displayed between Mondale and British Prime Minister James Callaghan did not dilute the severity of the British warning of likely trouble ahead in both southern Africa and the world economy.

Callaghan, who announced that he had accepted an invitation from Mondale to visit President Carter in Washington March 10 to 12, told reporters that he believes that 1978 could be "one of the most difficult years the world has seen" in economic terms.

British sources said Callaghan also warned Mondale that the Carter administration must stiffen its stand in southern Africa to persuade Rhodesian Prime Minister Ian Smith that the United States will not, under any circumstances, back him if the racial conflict in that country intensifies.

In their joint press conference, Mondale reiterated the administration's position of "standing fully behind" the now-stalemated British initiative to negotiate a timetable for black-majority rule of Rhodesia.

Neither Callaghan nor Mondale went into detail on the Rhodesian disscussions, but well-informed British sources said their officials had told Mondale that they believed that Smith broke off negotiations earlier this week in part because he believed that the United States would help him stem the threat of takeover by Marxist-oriented blacks.

They said, according to these sources, that they hoped that Andrew Young, the new U.S. ambassador to the United Nations, would avoid any calls for sanctions against South Africa, because that country is a key to restraining Smith from provoking a confrontation.

Mondale was questioned at the press conference about a reported comment by Young, featured in today's British press, that the Cuban troops in Angola have brought a "certain stability and order" to that country.

The comment made Tuesday in a CBS television interview, was described by the Daily Telegraph correspondent as indicating that "Mr. young might be poorly equipped to handle debates in the Security Council."

Mondale sidestepped any direct response to Young's words but defended the former Atlanta congressman and key black supporter of Carter as a "very effective leader and counselor in our common effort to bring about a responsible solution" to the problems of southern Africa "within the principle of majority rule."

Callaghan, discussing the international economic crisis, told Mondale:

"The most worrying aspect of the situation in the world today is that while there can be a reasonable prospect of growth in the United States and the Federal Republic of (West) Germany this year - not much here, because we're following a different policy - 1978 could be one of the most difficult years the world has seen in terms of growth. We could have large unused resources and large unemployment."

Callagahan, already beset by record unemployment at home, thus lent his support to Mondale's own urgings that West Germany, Japan and the United States should make a major joint stimulative effort this year to avert a worldwide recession.

Mondale, the son of a Methodist minister, began his day in Rome with a one-hour audience with the Pope in the ornate papal library.

The pontiff said he welcomed Mondales's diplomatic mission to Europe in the first week of the new administration because American foreign policy has "great repercussions . . . for the entire world. We are pleased that this policy is based on the desire to promote peace and international cooperation.

The pope added: "It is with optimism that we note the commitment of your President in favor of the reduction of weapons, particularly nuclear weapons."

Mondale responded: "Your warm and human words . . . will help the administration be launched in pursuit of justice, peace and moral works."

During the hour of private conversation that preceded the formal exchange of remarks, the Pope told Mondale that he had the same feeling about the Carter administration as he had had about that of John F. Kennedy.

According to Mondale's press secretary, Albert Eisele, who relayed Mondale's recollection of the conversation, the Vice President replied: "I am of the Kennedy generation. I have the same hopes for our administration."

The exchange of gifts with the Pope that concluded the audience produced a slight embarrassment for Mondale. The pontiff presented the Vice President with a bas-relief and several books and medals, including a souvenir medal of his 1965 visit to New York, which the Pope described as "a numismatic rarity."

Mondale reciprocated with one of the Carter inaugural medals, but told the Pope that the copy of the President's inaugural address he had intended to present would have to be sent along later beacause "my efficient staff work left in the airplane."

There was confusion, too, at the arrival ceremonies at London's Healthrow Airport. A London drizzle turned into a driving rainstorm as Mondale was welcomed by retiring U.S. Ambassador Anne Armstrong and British Foreign Secretary Anthony Crosland.

Replying the Vice President momentarily forgot Crosland's name, glanced down at his water-soaked notes to find it, and then continued to talk in competition with the whine of two taxing jets.

When the second plane interrupted his remarks, Mondale ad-libbed the addition of "airport noise control" to the list of issues he wanted to discuss with Callaghan and Crosland.

Crosland, perhaps thinking of the unresolved question of U.S. landing rights for the Anglo-French Concorde, stood unsmiling as the rain eradicated the crease in his suit.

In London, Mondale made emends to Portuguese Prime Minister Mario Soares, who had been pressing for inclusion of a stop in Lisbon on this trip.

The Vice President waited 20 minutes while a call was put through to Soares, and asked reporters to remain in his suite while he expressed regrets at being unable to visit Soares personally.

"The President asked me to express to you our support and admiration for what you and the Portuguese people have accomplished," Mondale said.

"Your magnificent efforts to set up democratic institutions have inspired all of us and we want you to know how deeply impressed we are . . ."