A Palestinian police chief has vowed to find three kidnapped Britons and says he will use force if necessary.
Hugh and Helen Burton had been visiting their daughter
But Alaa Hosni said there had been no contact with the unknown group responsible for abducting Kate Burton, 24, and her parents in Gaza.
The Muslim Council of Britain and the Palestinian Authority have condemned the kidnap of the British human rights worker and her parents.
Roadblocks are in place around Rafah where the three were taken.
British officials have told the BBC that they believe the trio are being held in southern Gaza, and think it likely they are being treated well and will be released unharmed, based on past experience.
A team of six British diplomats are in Gaza and Foreign Secretary Jack Straw is planning to raise the incident with Palestinian leader Mahmoud Abbas.
With the unusual lack of contact and strong denials from the larger militant groups, there is speculation that a small group may be behind the kidnapping.
The al-Aqsa Martyrs Brigade and Hamas - both responsible for suicide bombings in Israel - have called for the release of Ms Burton and her parents Hugh and Helen, known as Win, who come from Newbury, Berkshire.
Mr Hosni, head of police in the West Bank and Gaza, said: "Up to this point there have been no negotiations with the kidnappers. We don't know who they are.
"We're still searching and, God willing, we will catch the kidnappers as soon as possible.
"We'll deal with the situation according to circumstances. If we're obliged to use force we will use it to release them.
"But, God willing, we'll succeed in releasing them peacefully. We work to release these people because they're our friends and part of us. These people have been struggling for the Palestinian cause."
In a statement, a masked fighter from the al-Aqsa Martyrs Brigade said the kidnapping "harms the resistance effort".
Colleagues said they were worried about Ms Burton
Hamas also called for the Burtons' release, while Palestinians demonstrated to vent their anger.
"Mrs Burton, Kate's mother, has been active in the inter-faith movement in the UK and Europe for many years," said Sir Iqbal Sacranie, Secretary-General of the Muslim Council of Britain.
"The family's abduction and exposure to danger is absolutely unlawful, totally unjustified and counter-productive."
Analysts say kidnappings of Westerners in Gaza usually end with the hostages released quickly and unharmed.
Gunmen stage the abductions to attract attention, embarrass the Palestinian authorities, or raise money.
BBC security correspondent Frank Gardner said it was unusual for the kidnappers to have remained quiet and that the Palestinian police were working hard to trace the Burtons, who were likely to still be in Gaza.
He said there had been more than a dozen kidnappings since August but most were similar to those in Yemen in the late 1990s, when hostages were treated well while demands were met.
"It only went nasty if there was a big shoot-out. These comments that we've heard from the chief of police down in Gaza that they might have to resolve this by force are rattling a few people," he said.
"Inevitably people are saying, could it be al-Qaeda? But I think it is a little too early to say that and I think it would be unlikely."
There has been anger over the deteriorating security situation in Gaza, with 100 police officers demonstrating at the border crossing with Egypt at Rafah to protest against the killing of an officer.
Kate Burton's family described her as "a warm and loving person" who works as a volunteer in the Middle East.
In a statement on Thursday, the Burton family said: "We are a close family and are naturally deeply concerned about our parents and sister.
"Kate is a warm and loving person and has been working as a volunteer in Gaza for the past year trying to do what she can to help the situation there.
"We are grateful for the help and messages of support that we are receiving."
It is understood that Ms Burton, who speaks Arabic, as well as fluent French and Spanish, was showing her parents around Rafah, near the border with Egypt, when the kidnappers struck.
Michaela Meeraus, 22, from Oxford, a friend of Ms Burton's from university, told the BBC she was a passionate person who had an interest in the fate of the Palestinians.
Ms Burton had studied Hebrew and Arabic and her interest in the region had been fuelled by a stay in a kibbutz, she said.
"She is a very genuine, honest, person," Ms Meeraus said, "always really interested in meeting people - speaking several languages and having lots of international friends.
"The fact that she speaks Arabic and is with her parents probably comforts her a little bit."
It is understood Ms Burton had left her job with the UN in Gaza after it pulled all non-essential staff out because of the threat of kidnapping.
She continued to work in the area at the al-Mezan Centre for Human Rights as an "international co-ordinator".