Secretary of State George P. Shultz, welcoming a new public statement on arms control by Soviet President Konstantin U. Chernenko, called yesterday for a return to the "private processes of diplomacy" in order to work concretely toward new U.S.-Soviet agreements.

Shultz was reacting to the Soviet leader's written answers to questions from NBC News diplomatic correspondent Marvin Kalb, which were made public on the network's "Nightly News" broadcast last night.

Chernenko identified arms control as the top priority in relations between the two nuclear superpowers and said the Soviet Union is prepared to work "vigorously" toward agreements.

Shultz and several other experts said the tone of the Chernenko statement was positive, though it did not seem to advance Moscow's substantive positions as stated previously.

Some of Chernenko's points seemed to answer statements or proposals from Washington in recent weeks. For example, the Soviet leader wrote that "we have proposed practical, I emphasize, practical ways" to achieve agreements. This appeared to be an answer to recent U.S. demands for practical and concrete steps by the Soviets to advance arms control.

At another point, Chernenko wrote: "The task is not to establish some sort of a formal set of priorities, not to arrange a sequence of issues, depending on individual events." This appeared to be addressed to the U.S. proposal for "umbrella talks" conceived as the first step toward reopening substantive arms-control negotiations.

Chernenko repeated in summary form Soviet proposals made in his interview one month ago today with Washington Post correspondent Dusko Doder in Moscow. As formulated yesterday, these are "concluding an agreement on the prevention of militarization of outer space, a quantitative and qualitative freeze on nuclear weapons, and completing the work on an agreement providing for a complete and general ban on nuclear weapons tests."

The reformulation omitted his previous challenge to ratify two treaties limiting underground nuclear tests. The treaties were signed in 1974 and 1976, but have not been ratified by the Senate.

In a move possibly related to this challenge, Shultz last week reiterated the administration's appeal to the Soviets to accept an exchange of experts at underground nuclear test sites.

"We're seeing results, we're seeing progress" toward discussions with the Soviets, Shultz said yesterday. He said the next step was for diplomats to "really sit down in a small group and work concretely on problems and look for real results."

Chernenko said he did not believe that "conditions are now ripe" for a summit meeting with President Reagan.

White House officials, meanwhile, said the nature of the U.S. representation at initial arms-control discussions with the Soviet Union remained an open question until some clear indication was received about Soviet views.

"The president is willing to consider an overall coordinator, who would be a full-time person and work with Shultz across the board, a person with lots of clout," said a White House official.

White House spokesman Larry Speakes, responding to a Washington Post report that opposition from the State and Defense departments has thwarted the idea for an "arms-control czar," said Reagan had not ruled out any possible versions of the new position. Other officials continued to say that appointment of a "czar" with extraordinary powers to break the internal deadlock on arms control was unlikely.