Among those arrested was Benzi Gopstein, a prominent leader of the Israeli extreme-right group Lehava.
Arrests and searches for evidence were carried out simultaneously at addresses in Jerusalem, northern and southern Israel and in Jewish settlements in the occupied West Bank, police said.
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"Fifteen suspects known to the police as active in the Lehava organisation were arrested or detained for questioning during the night as part of a police investigation on suspicion that they acted to locate and threaten (Arab) minority members with connections to Jewish young women or girls," a police statement said.
Five of the suspects were later taken for remand hearings, police said.
Speaking to reporters at his hearing at Jerusalem magistrates' court, Gopstein said he was arrested for telling a Jewish woman that she should not date an Arab man, insisting he did no wrong.
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"Lehava operates within the limits of law only," he said. "It's all nonsense."
The court put Gopstein under house arrest, while the remand of two others was extended by two days.
The rest were allowed to return home, Haaretz newspaper said.
Lehava opposes inter-marriage. In August 2014, its activists staged a rally where racist slogans, including "Death to Arabs!", were shouted at the wedding near Tel Aviv of a Muslim man and Jewish woman.
Arabs account for some 17.5 percent of Israel's eight million population, and are descendants of Palestinians who remained on their land following the creation of Israel in 1948.
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In April, six Israelis, including two soldiers, were arrested for alleged racist attacks against Arabs with knives and other weapons and charged with "terrorist" offences.
Police said they were influenced by a Lehava video.
Gopstein was also questioned by police in 2015 after he condoned torching churches in Israel, in accordance with a mediaeval Jewish commandment to destroy places of idol-worship.
The police statement said that the latest arrests were the result of an undercover investigation.
"It uncovered organised and pre-meditated activity believed to have been carried out by the suspects, known members of Lehava," it said.
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