Taking another cue from the book of democracy, Lech Walesa, Poland's independent union chief, tried some good old-fashioned political stumping this week, setting off on a sort of campaign swing through the mines, millworks and hinterlands of southern Poland.

In a country whose leadership tends to see such Western-style politicking as frivolous extravaganzas best left to the imperialists, Walesa's traveling caravan of aides, fellow independent union organizers and press corps looked all the more remarkable.

But beyond its novelty, the five-day tour that just ended demonstrated widespread popular support not only for Poland's new labor movement but for the 37-year-old Walesa himself.

The trip was the first time Walesa had ventured out of Gdansk to go anywhere but Warsaw since he became a national figure by leading the shipyard strike in Gdansk that won for Polish workers the right -- unprecedented in the Soviet bloc -- to form independent trade unions.

The new unions have sprung up based largely by regions rather than professions and have united for security purposes in a loose federation named Solidarity that is headquartered in Gdansk, under Walesa's leadership. The organizational success of the regional branches so far varies, with more industrialized and populated areas showing the greatest strength.

Significantly, Walesa chose to travel south, through Poland's militant mining area around Katowice and into less industrialized mountainous parts below Krakow, there especially to give added support to local organizers and to calm fears of those people still worried about the consequences of signing up for membership in the new unions.

Within the movement, meanwhile, Walesa appeared to be struggling with radical forces who are advocating another strike in order to keep pressure on the Warsaw government to meet worker demands.

A national meeting yesterday of Walesa and other Solidarity leaders in the mining town of Jastrzebie exposed a conflict of opinion over the movement's future tactics.

Of central concern to the new union is what to do to end a four-week impasse with the government, which has delayed registering the national organization, raising several objections to Solidarity's proposed charter.

A strong hint that a compromise may be in the works emerged today when the Warsaw court that is handling the registration invited Solidarity representatives to a meeting Friday.

Against this tense background, Walesa appeared to be siding with the moderates. Repeatedly on the tour he downplayed the need for another strike, calling it "a dangerous weapon" and suggesting alternatives.

He said, for example, that if the government did not allow the new unions greater access to the mass media -- a running complaint -- workers might decide to stop paying their television tax and boycott newspapers.

In any case, Walesa said he did not intend to wait for the government to formally register Solidarity but would simply assume it would be done and proceed with organizing the movement's first elections.

Everywhere Walesa traveled, he was given celebrity treatment.

The people in Krakow, a center of Polish culture and once the seat of Polish Kings, crowded the ancient Wawel Cathedral on Sunday morning to watch Walesa attend mass and receive communion. The sermon, attuned to his visit, was on the meaning of the word "solidarity."

Afterward, Walesa was carried on the shoulders of workers for two miles through city streets to the memorial of Tadeusz Kosciusko, who in March 1794 swore he would lead Poland's peasants in rebellion.

Walesa, laying flowers on the memorial, echoed Kosciusko's oath, saying, "I swear I won't let you down."

With a cold rain falling, he drove on to address thousands in an ice rink in the mountain town of Nowy Targ, to stand before a sea of unbrellas in an open amphitheater in Nowy Sacz, and, at popular request, to trot a lap around a soccer stadium in Tarnow so that all in the stands could get a close glimpse of him.

He also met with workers in Kotowice and visited Poland's holy shrine at Czestochowa. While people waited for him, they sang religious hymns -- unthinkable in such public gatherings a short time ago and now a sign of the new self-assertiveness felt by many Poles.

At each stop, Walesa was showered with gifts. Notorious during the summer strike for wearing the same brown suit every day, he disclosed in Nowy Targ that he now has five gift suits.

"I don't keep them all," he said of the gifts. "I give some to my friends.

I don't do this for money."

His basic message was that he had come to serve workers, not to lead. "You know how to do the job best," he said at Nowy Sacz. "I wouldn't like people in ten years to say there was a man once named Walesa who promised lots of things."

Walesa was frequently asked about the new movement's relationship with Poland's dissident groups, specifically with the Social Self-Defense Committee, known by its Polish acronym KOR.

He said there are people in KOR who were his friends, who had helped him when he was fired in 1976 and again last year. Walesa said he would not abandon his friends. But he also said that Solidarity was taking advice from two other groups -- one a panel of experts headed by the Catholic intellectual leader, Tadeusz Mazowiecki, and the other the Catholic Church.

Commenting on the government's campaign against corruption -- part of the Warsaw leadership's effort to renew public confidence in central authorities -- Walesa said, "This is not the time to put people in prison. "I think the best thing would be for them to write on a piece of paper all they took illegally and just get rid of it."

At another point, he said, "We're not dangerous. All we want is to lead a normal life and have production serve us. Right now, we're not sure who it serves."