Their captors released a video shortly before freeing the family
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Top Palestinian negotiator Saeb Erekat has said the abduction of foreigners like the UK's Burton family in the Gaza Strip hurts his people's cause.
"We urge all Palestinians to make this the last such despicable act that harms and destroys Palestinian interests," he told the BBC.
The kidnappers have denounced the UK and threatened in a video to make further abductions.
Kate Burton and her parents were freed unharmed after two-and-a-half days.
The 24-year-old, who is now in Jerusalem with her parents, told the BBC they had been treated well by their kidnappers.
New threat
Speaking to BBC News 24, Mr Erekat agreed that there was a "very difficult" situation in the Gaza Strip.
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Kate remains committed and passionate about working alongside the Palestinians
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"I hope this will be the labour pains before the election that will take place on 25 January," he said.
The polls would, he added, be the Palestinian Authority's way of "restoring law and order and the one authority under one government".
Mr Erekat said every possible effort had been made to locate the three Britons including "house-to-house searches, area-to-area searches, town-to-town searches".
Asked if any deal had been struck to secure the Burtons' release, he said he did not have enough information to comment though he did not think so.
The kidnappers, a previously unknown group called the Mujahadeen Brigades, said in their video they would take more hostages if the UK did not do more to help the Palestinians.
In total, 14 foreigners were kidnapped in the Gaza Strip this year, a clear sign of the mounting chaos, the BBC's Richard Galpin reports.
It is likely to get worse as tensions mount between the many different Palestinian factions prior to the elections in Gaza and the West Bank, our correspondent adds.
'Not a bad word'
Ms Burton told the BBC she and her family had been moved three times in two days by their captors, who remained masked throughout.
She spoke of her sadness that her parents had had such a "desperate experience" during their visit to Gaza but said she hoped to continue her human rights work there.
Ms Burton, who works for the Palestinian Al Mezan Centre for Human Rights, also told the BBC Arabic service she and her parents had been held in Rafah, southern Gaza.
She added that she could not say a bad word about her captors, who always asked whether they needed anything.