The new Soviet leader, Mikhail Gorbachev, has taken his campaign for modernization of Soviet society to the grass-roots level by spending the past two days in a heavily industrial section of Moscow to talk directly with workers, shoppers and other residents.

Photographs displayed on Soviet television late tonight revealed a new style of leadership, with the 54-year-old Gorbachev looking like a western politician visiting his district before an important election.

After visiting supermarkets and food shops and touring a housing complex, Gorbachev called on a young couple in their apartment to discuss their problems and "their hopes for the future" over a cup of tea.

It was the kind of performance not seen here since the days of Nikita Khrushchev.

Gorbachev's predecessors frequently visited various factories, but such visits were carefully prepared in advance to include a political rally that provided them with an audience for announcing major policy decisions.

Only Gorbachev's political mentor, the late Yuri Andropov, attempted to reach ordinary citizens directly when he sought to mobilize the country for economic changes. However, Andropov's illnesses precluded a vigorous personal campaign of the kind staged by Gorbachev yesterday and today.

An account of Gorbachev's tour of the Proletarski district of Moscow distributed by the official news agency Tass indicated that his main focus during conversations was on improved labor efficiency, greater discipline, financial incentives and modernization of industrial and service facilities.

In a departure from previous practices, Gorbachev went to the shop floor of a large automobile factory to discuss "problems" and to talk about workers' salaries and living conditions. Tass said that during one meeting "it was proposed" that experienced workers with long tenure be given higher salaries.

Soviet television quoted Gorbachev as saying that it was essential that workers be encouraged to show initiative and to seek "bold" solutions that would raise productivity. Tass said Gorbachev also urged wider use of "economic incentives" to that end.

During a visit to School No. 514, Gorbachev was quoted as discussing with teachers the main aspects of educational reforms and "the use of computers in the teaching process." The Soviet leader also raised the possibility of increased salaries for physicians during a visit to City Hospital No. 53, which is located in the Proletarski district.

Soviet doctors receive notoriously low salaries, well below the average wage of industrial workers. The workers, by and large, receive salaries that do not differ according to their performance.

Tass said Gorbachev's discussions also included an exchange of views on ways to "perfect the economic mechanism," a code phrase for economic reforms.

The Communist Party newspaper Pravda revealed two days ago that 240,000 industrial managers and officials in Moscow are currently taking courses to improve their "economic knowledge." Gorbachev's two-day tour indicated that the new leader was seeking support for a package of economic reforms developed during Andropov's brief rule to revive the economy.

Tonight's announcement of Gorbachev's surprise tour of the Proletarski district coincided with an official report indicating a slowdown in Soviet industrial production.

According to Tass, Gorbachev explained his tour by telling his interlocutors that the Soviet party "constantly takes counsel with the people."

"Society is now faced with great tasks to accelerate the socioeconomic development of the country," Gorbachev reportedly said. He called for increased efforts to step up production, raise its quality, modernize plants and "show creative initiative."

During a visit to a supermarket, Tass said, Gorbachev "conversed with customers about the satisfaction of their requirements." He was said to have shown interest in "suggestions" from shoppers on how to improve things.

Television photographs showed the new leader talking to a lathe operator at her job, laughing heartily with a group of workers, showing serious concern as he listened to a man apparently making "suggestions" for improvement, and visiting a classroom.

Gorbachev also visited the apartment of Tamara and Vyacheslav Nikishin and listened to them as they "related how they live and work and shared plans for the future."