Gaza Strip on Friday by the Palestinian gunmen who kidnapped them two days earlier.

A previously unknown group calling itself Brigades of the Mujahideen-Jerusalem said it seized Kate Burton, her father Hugh and mother Helen to demand British and European pressure on Israel and freed them as a gesture of goodwill.

The Burtons passed through Gaza City briefly before being whisked away toward Israel in diplomatic cars with darkened windows.

"They are well and in good spirits. They are currently with officials from our Consulate General in Jerusalem," said a statement from the British Foreign Office.

"She was not hurt, her parents were okay and she plans to visit Gaza next week," said Adnan Hajjar, a colleague of Burton's. "Kate said she was sorry that she could not make it to the hotel to greet everybody."

In a video released to media, a masked gunman read out a message standing next to Kate Burton, who appeared with her hands behind her back.

"We have decided to pardon the three Britons as a gesture of goodwill in return for a seriousness in answering our demands," the gunman said.

Burton and her visiting parents were seized in the chaotic southern town of Rafah on the Egyptian border on Wednesday. Kidnappers, armed with automatic rifles, pulled over their car and bundled them into another vehicle that sped away.

The political demands and Islamist tone of the captors were a marked departure from previous kidnappings in the Gaza Strip, whose perpetrators tended to be seeking jobs or the release of prisoners and set free their hostages within hours.

The fact the kidnappers made no contact for two days had raised concerns for the Britons' safety.

"We thank everyone who has worked so tirelessly toward this moment, especially Kate's colleagues and friends in Gaza, who kept all our hopes up throughout this ordeal," said a statement from the Burton family released through the Foreign Office.

The kidnappers said that they wanted British and EU pressure on Israel to end the "no-go zone" it imposed in northern Gaza this week to stop rocket fire, to free prisoners, pull back troops in the occupied West Bank and end assassinations of militant leaders.