Vice President Mondale said yesterday he will carry a message of the need for "across-the-board" restraint on domestic spending to the Democratic Party's liberal constituencies in coming weeks. He predicted most of them will accept President Carter's decisions to hold down spending, even on programs that have been at the heart of the Democratic platform.

In an interview with The Washington Post in his White House office, Mondale said the current fiscal 1980 budget review sessions have left him with "a sobered realization . . . of the very real and tight budget constraints on all aspects on programs" the fight on inflation will require.

Mondale, considered by many the most important liberal voice in the administration, will test his hold-the-line rhetoric before an important and skeptical audience next Tuesday, when he speaks for the White House to the U.S. Conference of Mayors convention in Atlanta - 24 hours after Sen. Edward M. Kennedy (D-Mass.) addresses the same audience.

Key mayors have complained already that budget-cutting is a threat to Carter's new urbon policy, especially in the wake of local tax reductions ordered by such measures as California's Proposition 13.

But Mondale said, "We're not doing our traditional constituents any good if we raise expectations unrealistically or purse budgetary policies that reignite inflation."

"I consider myself a progressive," he said, "and I don't see anything inconsistent between those general social objectives and the need of prudent economic policies to avoid inflation."

The vice president said he thought the Carter economy moves would be accepted by liberals because "within the limits of our budgetary situation, we're making choices in a progressive way," still emphasizing education, health and "sound programs for humane objectives."

But he conceded that budgetary restraints will have an impact on the soon-to-be announced Carter design for a national health insurance program, long a key objective of Democratic liberals.

Mondale also defended Carter's warnings to the Soviet Union and Cuba on their actions in Africa - also a subject of some criticism from liberal Democrats.

Speaking of Africa, he said "the Russians are trying to exploit differences and disputes wherever they can . . . The prefer to radicalize a situation rather than resolve it."

Asked how he assessed Soviet objectives in Africa, Mondale said, "I think they're trying to establish their influence and domination in as many places as they can . . . in the Horn, in Angola, in just about any place they can."

But the vice president said he thought the Soviet tactics may backfire. "There is a growing restiveness in Africa about Soviet and Cuban activities" reflected in the diplomatic cables he reads, he said.

Like Carter, Mondale discounted the possibility of major American countermoves against Soviet-Cuban actions in Africa, but said that if countries friendly to the West "were threatened, we might have to tilt' current U.S. economic aid programs "more toward the military side."

"There is no intention of establishing a military presence there," he said.

Although he delivered a speech to the United Nations disarmament conference sharply critical of the Soviet military buildup, Mondale has not been publicly vocal in the recent debate over U.S.-Soviet policy.

He was not among the five senior administration officials who met with Carter on the Sunday before the president's Annapolis address restating the administration policy on relations with Russia.Mondale laughingly explained, "I was at a crucial pregraduation event for my daughter."

But the vice president said he made suggestion for the speech, and he strongly rejected criticism that the address reflected conflicting policy advice to the president from advisers favoring a conciliatory or a hard-line approach to the Russians.

"Realism," he said, requires that the administration emphasize both its desire for a strategic arms agreement with Russia and the "additional difficulties" created for such an agreement by the Soviet arms buildup.

Asked if he thought the combination of domestic program restraints and a stronger anti-Soviet rhetoric would increase the risk of a challenge to the administration from the Democratic Party's left, Mondale said, "I don't think so, no. But I do think we've got to do our public education job."