NEUNKIRCHEN, WEST GERMANY, SEPT. 10 -- East German head of state Erich Honecker said today he believed that a normal border could be established in the future between the two Germanys, implying that his government might tear down the existing concrete- and barbed-wire barriers manned by guards who shoot people trying to escape to the West.

Honecker said the inter-German frontiers today are not "as they should be" because the two states belong to rival military pacts. But he said the border could become normal, like the frontier between East Germany and Poland, if the two Germanys continue the kind of "peaceful cooperation" begun this week with his unprecedented visit to West Germany.

The East German leader's statement appeared to mark the first time since Germany was formally divided in 1949 that East Germany's communist government has raised the possibility of removing the border fortifications that are the most dramatic symbol of the East-West division of Europe, West German government and diplomatic sources said.

Honecker made the startling pronouncement at a reception held in his honor at a community center here in southwestern Germany following his first visit in 39 years to the house where he spent his early boyhood in the nearby working-class village of Wiebelskirchen.

The West German government welcomed Honecker's statement as a sign that East Germany was moving in "the right direction." Honecker's statement corresponded to what was discussed in his talks in Bonn with Chancellor Helmut Kohl on Monday and Tuesday, a spokesman said.

There apparently were several catches in Honecker's offer, however, according to West German government sources and western diplomats.

Most importantly, his proposal that the inter-German border would become a fully recognized international frontier conflicts with West Germany's official position that the two Germanys someday will be reunited. In addition, Honecker seemed to suggest that the two Germanys would have to loosen their ties to their respective alliances, which could prove to be extremely difficult.

Finally, he did not specify how his proposal would affect the thorny status of West Berlin, a western enclave 110 miles inside East Germany whose security and administration is protected by France, Britain and the United States.

"The German Democratic Republic {East Germany} is an active member of the Warsaw Pact, and the Federal Republic of Germany {West Germany} is firmly anchored in the Western Alliance. Under these conditions, that the borders are not as they should be is only too understandable," Honecker said.

"But I believe that if we work together toward it, in accordance with the communique that we have just signed in Bonn {on Tuesday} and if, in connection with this, we demonstrate further peaceful cooperation, then the day will come when the borders will no longer divide us, but when the borders will unite us, as the border between the German Democratic Republic and the People's Republic of Poland unites us," Honecker said.

His statement, the top story on West German television news this evening, was described by a television commentator as "remarkable."

Honecker appeared to have chosen his words carefully, as his language left many important questions unanswered, diplomatic sources said. But they said he had made public "a new formulation" on a critical issue in inter-German relations.

The joint communique called for increased efforts by both Germanys to increase travel between them, expand trade and technical cooperation and have more sports and cultural exchanges.

Honecker spoke shortly after he was serenaded by a local left-wing band for which he was a drummer boy when he was growing up in Wiebelskirchen, a drab community of coal miners and steelworkers.

About 1,500 well-wishers lined the street outside his modest, two-storied boyhood home while he and his sister, Gertrud Hoppstaedter, who lives there, visited for 20 minutes. They were joined by some of his boyhood friends.

Earlier, the 75-year-old communist leader stood in silence in a nearby cemetery as he made his first visit to his parents' graves. The division of Germany had made it impossible for him to visit his hometown since 1948. His sister, who has visited him many times in East Berlin, is a member of the tiny German Communist Party.

Honecker may have timed his statement today for delivery here to avoid making it in Bonn, where it would have seemed to be a concession to the West German government, political observers said.

The favorable statement about inter-German relations also fit well in the emotional context of the long-delayed homecoming, they said.

In making the statement, the normally wooden Honecker appeared more lively in public than at any time since he arrived in West Germany on Monday.

"This is a Honecker that we haven't seen before," a television commentator said. He was "open, warm and spontaneous," she said.

West Germany's chief government spokesman, Friedhelm Ost, said that Honecker's statement showed that East Germany was "moving in what we regard as the right direction," West German radio reported.

Bonn Economics Minister Martin Bangemann said that the Honecker statement represented "considerable progress."