The three British hostages -- aid worker Kate Burton, 25, and her parents, Hugh and Helen -- were released late Friday and driven to Jerusalem in armored cars early Saturday. Kate Burton told the BBC she and her parents were moved three times during their abduction, but that the masked kidnappers treated them well. She said her parents were tired from the ordeal.

"We thank everyone who has worked so tirelessly towards this moment, especially Kate's colleagues and friends in Gaza who kept all our hopes up throughout this ordeal," the statement said.

A previously unknown group calling itself the Mujahedeen Brigades Jerusalem Branch claimed responsibility, threatening more abductions of foreigners if Israel doesn't abolish its "no-go" zone in the northern Gaza Strip. Israel imposed the off-limits area this week to prevent rocket fire, and has threatened to shoot anyone entering the zone.

The kidnappers said they released the hostages as a "goodwill gesture" after receiving assurances that Britain and the European Union would seek an end to the Israeli buffer zone. British officials, however, denied that a deal had been struck.

The kidnappers said they would seize international election observers if their demands were not met. Mathias Eick, a spokesman for the observers, said Saturday that the group did not plan to change its deployment ahead of Jan. 25 parliamentary elections, but would keep assessing the risk.

Most of those engaged in violence in Gaza recently have ties to Palestinian leader Mahmoud Abbas' Fatah party, fueling voter resentment less than a month before the vote.

Fatah has been the dominant Palestinian movement since it was founded four decades ago, but is facing a strong challenge by the Islamic militant group Hamas, which is competing in a general election for the first time. Hamas promises voters clean government, in sharp contrast to Fatah's corruption-tainted image.

In newspaper ads published Saturday, Fatah's top candidate, jailed uprising leader Marwan Barghouti, urged voters to give the party another chance -- a rare admission of failure.

"We do not hesitate to apologize to the Palestinian people for the mistakes that have been committed in recent years ... and I call upon the Palestinian people to renew their confidence in Fatah and to give Fatah a new opportunity," said Barghouti, who is serving five life terms in an Israeli prison for involvement in attacks on Israelis.

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