Palestinian authorities have stepped up work to find a kidnapped British human rights worker and her parents in Gaza.
Kate Burton was working with a human rights group
Kate Burton, 24, was abducted on Wednesday, along with her mother and father, who were visiting her.
Road blocks to inspect traffic have been set up in Rafah, where they were snatched, and nearby in Khan Younis.
Palestinian officials said they were in contact with armed groups, but did not know where the family was. Protests for their release have been held in Gaza.
The BBC's Alan Johnston in Gaza said there had been unconfirmed reports of contact with the kidnappers.
In a statement, 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."
Taken from car
They appealed for privacy, saying the situation was sensitive and they did not want to make any further comment.
Frank McGinley, of the British consulate general in Jerusalem, said officials were investigating.
Efforts are ongoing to find out whether the kidnappers are asking for a particular local problem to be resolved or whether there is a wider issue.
Palestinian NGO workers demonstrate about the kidnapping
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.
The three were travelling in a car 200m from the border when they were approached by gunmen at about 1600 (1400 GMT) on Wednesday, said police in Rafah.
The kidnappers forced them to leave their car and go with them. Security vehicles gave chase but eventually lost the car.
The abduction of foreigners is not unusual in the area. Hostages are usually released unharmed within hours.
Last week, two foreign teachers were taken by gunmen but quickly freed unscathed.
Generally, militant groups use the hostages to press the Palestinian authorities for money, jobs or the release of prisoners.
It is understood Ms Burton had left her job with the UN in Gaza, after it pulled all non-essential staff out due to the threat of kidnapping.
She continued to work in the area at the al-Mezan Centre for Human Rights as an "international co-ordinator"
Nafiz al-Mahdoun, from the centre, told BBC News their missing volunteer worked for the group for the past three months but had been on holiday since 22 December.
"Our organisation, in co-operation with the security and police people, are looking everywhere in Gaza to find them and see what is going on."
Ms Burton was at the European School II (Woluwe) in Brussels from 1987 to 1999 before studying at the London School of Economics.
Afterwards, she worked with the UN in Gaza and intended to remain there for another year.
Michaela Meeraus, 22, from Oxford, a friend of Kate's from university, told the BBC she had had an email from Kate a couple of weeks ago, telling how she had been scared by recent Israeli missile strikes on Gaza.
Kate, she said, is a passionate person who had an interest in the fate of the Palestinians. When the UN project ended, she felt she should stay in the area to continue her work.
She had studied Hebrew and Arabic and her interest in the region had been fuelled by a stay in a kibbutz.
"She is a very genuine, honest, person," she said. "Always really interested in meeting people - speaking several languages and having lots of international friends."
She was optimistic about how Kate would deal with being held by kidnappers, but said she would probably be worried about her older father.
"She's a calm person but would be quite upset and emotional. The fact that she speaks Arabic and is with her parents probably comforts her a little bit."