The court in Nazareth in northern Israel extended Meir Ettinger's detention until at least Sunday, the sources said.
Ettinger, whose grandfather Meir Kahane founded the racist anti-Arab movement Kach, was arrested on Monday "because of his activities in a Jewish extremist organisation", a spokesman for the Shin Bet internal security service told AFP.
According to Israeli media, he was the brains behind a June 18 arson attack on a shrine in northern Israel where Christians believe Jesus performed the miracle of the loaves and fishes.
"All that is window dressing, there is nothing on file" connecting Ettinger to that crime, his lawyer Yuval Zemer told reporters after Tuesday's hearing, which featured a smiling Ettinger flanked by two courtroom guards.
Media reports said Ettinger could face a year of "administrative detention" under the government's harder line against "Jewish terrorists".
Israel normally applies the measure, which dates from British-mandated Palestine, against Palestinians, allowing renewable six-month periods of detention without trial.
Friday's attack, which killed 18-month-old Ali Saad Dawabsha, sparked an international outcry over Israel's failure to get to grips with violence by hardline Jewish settlers.
Dawabsha's parents and brother were badly burned in the attack and remain in a "critical" condition, a hospital spokeswoman said.
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