Gabriel visited the eastern German town near Dresden on Monday, in a show of support for the officials who faced violent protests by hundreds of far-right extremists over the weekend.
"We must not give even a millimeter to these people, who have spread out here during the last few days," Gabriel, who is also the German economy minister and the Social Democrat party chairman, said.
German Chancellor Angela Merkel also condemned the recent violence in Heidenau on Monday, via her spokesman Steffen Seibert .
"It is disgusting how right-wing extremists and neo-Nazis attempt to spread their idiotic message of hatred around an asylum shelter," Seibert told reporters, adding that Germany does not tolerate "hate-filled slogans or threats coming from drunken loudmouths" targeting refugees.
These comments followed fierce criticism in the press and from opposition politicians, asserting that Merkel had done too little to denounce the weekend's unrest. On Monday on Twitter in Germany, the hashtag #Merkelschweigt - which roughly translates as "Merkel stays silent" - was the most commonly used in the country, even after the chancellor broke this "silence."
The clashes in Heidenau began late on Friday, as the police were bringing asylum seekers to the town's refugee shelter. Anti-migrant protesters tried to block the roads and pelted the security forces with rocks, bottles and firecrackers.
The scuffles broke out anew on Saturday and Sunday night, and over 30 police officers have been injured during the last three days.
On Sunday night, the police intervened in stopping a fight between a group of leftists protesters, who came to the streets to show support for the refugees, and the right-wingers, a police spokesman said Monday.
Also on Sunday night, the police set up a perimeter around the Heidenau refugee center, checking the papers and frisking people approaching the building.
"We need such safety zones all over, because nobody can say where the next attack is going to happen," police trade union head Rainer Wendt said to the German "Rheinische Post" newspaper.
Wendt added that it was "repulsive if Nazis can hold their demonstrations and run wild right in front of the refugee homes."
The far-right extremists were "definitely from outside Heidenau," Heidenau's mayor Jürgen Opitz told German public broadcaster Deutschlandfunk on Monday.
The extremists in the area were connected and the riots in Heidenau were an example of "Nazi tourism," according to the mayor.
Opitz greeted Gabriel on Monday, saying that he was also looking forward to a visit from Chancellor Angela Merkel.
"I hope (…) to greet Mrs. Merkel here, in two days at the latest," he said.
The violence in Heidenau is only the latest example of racially-motivated attacks on refugee homes in Germany, with several housing facilities burned by suspected far-right activists during recent months.
A building was also destroyed by fire in Weissach, southwest Germany, officials said Monday. The building, which was empty at the time, was set to be converted to a refugee home. The authorities say it is too early to determine the cause of the fire.
Three people were arrested in Berlin on Friday in relation to a separate arson attempt in Bavaria.
dj/msh (epd, Reuters, dpa, AFP)