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With tensions high along the Gaza border, Israel said its aircraft attacked 10 sites in the Palestinian enclave in response to persistent rocket strikes on southern Israeli towns.
But Prime Minister Benjamin Netanyahu signalled that broader Israeli action was not imminent.
The burning-alive of 16-year-old Mohammed Abu Khudair, and the earlier murders of three kidnapped Israeli teenagers, have driven relations between Palestinians and Israelis to their lowest point since U.S.-backed peace talks broke down in April.
The security source gave no details about the suspects arrested in the investigation into the abduction and killing of Abu Khudair, other than to say they were Jewish and that police saw "nationalist motives" in the case.
Police spokesman Micky Rosenfeld said a gag order had been imposed on most details of the case, commenting only that police had arrested a number of Jewish people suspected of carrying out the killing.
Israel's Shin Bet security agency said the suspects were being questioned at one of its installations.
Despite the gag order, Israeli media said a court had ordered the suspects remanded into custody for eight days. Police declined to comment. Israel's Channel 2 television said the suspects were far-right extremists, among them minors, from the Jerusalem area and a nearby Jewish settlement.
Abu Khudair's burnt body was discovered in a Jerusalem forest on Wednesday. Palestinians believe he was the victim of far-right Jews avenging the kidnap-killing of the three Israeli teenagers who disappeared while hitchhiking in the occupied West Bank on June 12, and whose bodies were found last Monday.
Israel blames the deaths of Naftali Fraenkel and Gil-Ad Shaer, both 16, and 19-year-old Eyal Yifrah, on the Palestinian Islamist movement Hamas. The Gaza flare-up began in mid-June during Israel's search for the teenagers in the West Bank, when it arrested some Hamas members.
Hamas has neither confirmed nor denied involvement in the killings of the Israelis.
Netanyahu, speaking at a visit to the Fraenkel family, demanded Palestinian leaders do everything to find the killers of the young Israelis.
He said the Palestinian self-rule government in the West Bank was "obliged to do everything in its powers to find them ... just as our security forces located the suspects in the murder of Mohammed Abu Khudair within a matter of days."
An autopsy attended by a Palestinian pathologist showed soot in the teenager's lungs, indicating he was still alive when he was set on fire, the Palestinian attorney general said.
Palestinian President Mahmoud Abbas said he sent a message to United Nations Secretary-General Ban Ki-moon urging the formation of an international investigation committee into "terror crimes conducted against our people, including the burning alive of Mohammed Abu Khudair."
Netanyahu said Abu Khudair's killers would face "the full weight of the law," adding that in Israeli society "there is no place for such murderers."
"We won't let extremists on either side set the area on fire and lead to bloodshed," Netanyahu said, while also condemning violent protests by some Israeli Arabs in northern Israel.
Dozens of protesters threw stones at passing cars for a third day in Israel's Galilee region, where a majority of Israel's Arab citizens live, this time targeting a highway in the Haifa area where a fatal accident was reported, police said.
In remarks to his cabinet earlier on Sunday, Netanyahu pledged "to do whatever is necessary" to restore quiet to southern Israeli communities that have come under rocket attack from the Gaza Strip, where Hamas is the dominant force.
He cautioned against any rush toward wider confrontation with the group, whose arsenal includes long-range rockets that can reach Israel's heartland and its business capital, Tel Aviv.
The Israeli military said more than 20 rockets fired from Gaza struck inside in Israel on Sunday. There were no reported casualties.
"Experience has shown that during moments like these, one must act in a level-headed and responsible manner and not hastily," Netanyahu told his cabinet, in broadcast remarks.
Israel beefed up ground forces along the Gaza frontier on Thursday, a deployment seen as sending a message to Palestinian militants that an invasion was an option if rocket fire did not stop.
Palestinian-American Tariq Khdeir, 15, a cousin of the slain Palestinian teenager, was arrested by Israeli border policemen, who his family said beat him severely, during a protest on Thursday in East Jerusalem.
An Israeli court on Sunday ordered Khdeir released from jail and placed under house arrest for nine days. His mother said the family planned to return to Tampa, Florida on July 16.
The United States has called for an investigation, and Israel's Justice Ministry said the police internal affairs office was looking into the incident.