Four more people were seriously injured as a result of the accident, which happens in Núpsvötn, south of the Vatnajökull glacier at about 10am today.
Four adults and three children were in the 4×4 Toyota Land Cruiser it plunged more than 26ft off a bridge.
The accident happened at around 9.30am on Thursday when the Toyota Land Cruiser crashed through a railing on a one-lane bridge in the south of the country before falling around eight metres onto a river bank.
Icelandic broadcaster RUV said there was no indication as to the condition of the survivors.
RUV reported “all available medical services from South Iceland” had been called for.
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As a result of the accident, which occurred Suðurlandsvegur by the bridge over Núpsá, east of Kirkjubæjarklaustur, the road will be closed for an “indefinite period”.
Icelandic website www.frettabladid.is said a Coast Guard helicopter had landed at Landspítali in Fossvogur with the British tourists.
Two of the injured people are understood to be children.
Three others have died including one chlld, police superintendent Sveinn Kristján Rúnarsson confirmed.
The website added: “He says it is probably a family case but the police have not yet been able to talk to the survivors. They were all transported by the Coast Guard’s helicopters to the hospital in Fossvogur.
“Two helicopters were deployed on the platform and one of them landed at Landspítali in Fossvogur just after 13 today. The other helicopter is still on its way.
Chief Superintendent of south Iceland Police Sveinn Kristjan Rúnarsson said the four injured have been taken to hospital with serious injuries, but added that “we haven’t been able to talk to them about what happened”.
Mr Rúnarsson said the police were still at the scene of the investigation and therefore still closed on the South Iceland road, which will probably be closed for the rest of the day.
Tour guide Adolf Erlingsson, who was among the first on the scene, told the Associated Press: “It was horrible.
“The car seemed to have hit the ground many metres from where it stopped. We struggled getting everyone out.”
It is unclear how the driver lost control of the vehicle.
Mr Erlingsson added: “Somehow the driver must have lost control of the car and it just went through the railing and crashed down onto the bank. It’s kind of sandy. It flipped over and was totally destroyed.
“Just before I arrived I was overtaken by a police car then when i got there there were two police cars and I got out of my van and went to see if I could help. There were just two police officers and me to begin with.
“We tried to assess thew situation and see who was alive and who could help.
“When I got there four people were out of the car, one of them deceased, and there were three people trapped in the caer. I think two of them were deceased.
“Outside of the car the was one adult and two children semi-conscious.
“I talked a little bit to them. I tried to talk to the driver, calm him down, he was trapped inside the car. I said save your energy and we will try to get him out of there.”
(More to follow)