SEOUL (AFP) - Seven South Koreans who survived after their sightseeing boat capsized and sank in Budapest said help came too late as they waited trembling in the freezing river in the dark, Yonhap news agency reported on Thursday (May 30).

Seven South Koreans died and 21 others remain missing after the Mermaid boat collided with a much larger passenger river cruise ship on the Danube in the heart of the Hungarian capital on Wednesday.

"The current was so fast and people were floating away but the rescue team did not come," a 31-year-old woman, identified only by her surname Jung, told Yonhap at a Budapest hotel where the survivors were taken.

Sobbing, Ms Jung said she was taking photos on the deck at the time of the collision, adding: "I saw a big cruise ship approach us but didn't imagine it would crash into our boat."

She was among around 20 passengers snapping pictures of the night view of the city or preparing to get off the ship, as the cruise was nearing an end.

Ms Jung clung on to a rescue buoy and threw an attached rope to fellow passenger Ms Yoon, 32, Yonhap cited the woman as saying.

The women said tears streamed from their eyes as they saw the heads of other passengers popping above and below the water as they struggled to stay afloat.

"The boat flipped instantly and capsized," said Ms Yoon, who had been travelling with her mother.

In just seconds, everyone on the deck had fallen into the river, she added, saying around 10 others who remained in the cabin were believed to have been unable to escape.

The tourists - mostly in their 50s and 60s - were on a nine-day trip that included Croatia, Slovakia, Czech Republic, Hungary, Austria and Germany.

The youngest passenger aboard the sunken boat was a six-year-old girl travelling with her mother and grandparents. She remains missing.

The survivors said the rescue operation began too late, and raised questions over why the cruise went ahead in heavy rainfall.

"The relief team that showed up later just took people like me, who were already holding on to tubes, out of the water," said a 60-year-old survivor surnamed Ahn.

The tragedy comes five years after the Sewol ferry sinking in South Korea which killed more than 300 people in one of the deadliest maritime disasters in the country.

The 6,825-tonne Sewol was carrying 476 people - most of them high-school students on a school trip - when it capsized off the country's southern coast in April 2014.

Almost all the victims were children, many of whom obeyed orders to stay in their cabins as the vessel slowly sank, with the disaster blamed on a deadly combination of cargo overloading, an illegal redesign and poor helmsmanship.