MOSCOW (AP) _ Plainclothes agents backed by snowplows today broke up a demonstration on behalf of a jailed Jewish activist and roughed up Western reporters covering the protest. Police briefly detained 13 protesters.

About 20 people have been demonstrating at the Arbat shopping mall in central Moscow each day beginning Monday. They demand the right to emigrate and seek the release of Josef Begun, a Hebrew teacher who was sentenced in October 1983 to seven years in prison for ''anti-Soviet agitation and propaganda.''

During today's protest, uniformed police were stationed along the mall and in a nearby ally, but did not intervene until after the plainclothes agents moved in.

All of those detained by police - seven at the protest site and six on their way there - were released after a few hours. Six, including Inna and Boris Begun, the wife and son of the jailed activist, were fined about $77 for ''petty hooliganism.''

Foreign Ministry spokesman Gennady Gerasimov told reporters he didn't see the demonstration, but that if there was any violence, it was between protesters and a group of young toughs.

''The authorities did not touch the demonstrators,'' he said, referring to the men who halted the protest. He said he regretted that reporters were injured.

The duty officer at the district militia station said, ''there was no demonstration of any kind or any violence, just some hooligans disturbing the peace.''

Although Gerasimov denied authorities broke up the protest, it was clear at the scene that the plainclothesmen were not teen-age vigilantes. They were well organized and were backed up by snowplows and uniformed police.

The uniformed officers, normally quick to end street violence, did not make any move against the men in civilian dress who punched and kicked demonstrators and Western reporters.

Police detained Hartwig Nathe, correspondent for the West German news agency dpa, for about 45 minutes and confiscated his film. But a half-dozen Soviet men photographed and filmed the protest without any interference by police or the plainclothes forces.

Western television camera crews and correspondents who tried to photograph the protest were punched, kicked and knocked into walls by the plainclothesmen.

Three men tackled an Associated Press reporter who tried to photograph Boris Begun's detention, knocking him against a wall. Other government agents cut the cable on a television camera.

Authorities did not interfere with the protests on Begun's behalf Monday and Tuesday, but plainclothes agents shoved the protesters off the square Wednesday.

The protesters gathered again at the mall at 10 a.m. today and were quickly surrounded by at least 50 agents.

Throughout the 20-minute demonstration, two snowplows circled closer and closer to the group, herding them from one side of the mall to the other and finally helping the plainclothesmen force the demonstrators onto a side street.

The demonstrators said nothing. But a few began holding up signs that read, ''Free Josef Begun'' and ''Let us go to Israel.'' They were dragged off by plainclothesmen to a nearby alley where a squad of uniformed police waited with vans.

Boris Begun held up a sign that read, ''Free my father, Josef Begun'' and was grabbed by a half-dozen men who pulled him away, slapping and punching him as they went.

About six other plainclothes agents began fighting with the protesters, men and women who ranged in age from the mid-30s to a 78-year-old World War II veteran who wore a government medal on his chest.

On Tuesday, Gerasimov said Begun had declined to apply for a government pardon that freed 140 other imprisoned dissidents. Begun's family said they have no way of confirming the report.

Gerasimov said the cases of 140 other jailed dissidents were being reviewed.

But the demonstrators said the slight liberalization under Kremlin leader Mikhail S. Gorbachev has not extended to Jewish emigration.

''It's a crazy and horrible situation,'' said Irina Brailovsky, whose husband served four years in prison and exile on a conviction of anti-Soviet slander.

''It is an outrage that right now when democratization is declared to be taking place in this country, and we hope that it's so, nothing has changed for Jewish emigration,'' she said.

Several people in the crowd that broke up the protest shouted that the demonstrators were ''mocking our fatherland'' and ''insulting the Soviet state.''

One chanted, ''Jews, Jews,'' in German.