Budapest (AFP) - Hopes of finding survivors from one of Hungary's worst boat disasters were fading on Thursday, a day after a collision on the Danube left seven South Korean tourists dead and 21 other people missing.

The Mermaid sightseeing boat capsized and sank in just seconds after colliding with a much larger river cruise ship on a busy stretch of the Danube river in the heart Budapest in driving rain on Wednesday evening.

Thirty-five people were on board the Mermaid, most of them South Korean tourists including a six-year-old girl who was travelling with her mother and grandparents and remains missing.

The boat's captain and a crew member -- both Hungarian -- are also missing following the disaster in which only seven people aboard the Mermaid are known to have survived. 

Police said on Thursday that the captain of the larger ship, the 135-metre four-storey Viking Sigyn, had been taken into custody and "questioned as a suspect... in relation to 'endangering waterborne traffic resulting in multiple deaths'."

"After being questioned, 64-year-old Yuriy C., a resident of Odessa, was detained and a request for his arrest has been made," the statement added.

Police and army boats mounted a second night of search activity on the chilly and fast-moving river but the operation has been complicated by high river levels and a strong current after weeks of heavy rainfall.

At the time of the collision, most passengers were sheltering from heavy rain inside the boat, Mihaly Toth, a spokesman for Mermaid owner Panorama Deck told weekly magazine HVG.

Toth described the chances of further survivors being found as "very slim".

Police said three bodies had been found several kilometres south of the disaster site.

"The current was so fast and people were floating away but the rescue team did not come," a rescued 31-year-old woman identified only by her surname Jung told South Korea's Yonhap news agency.

The Viking Sigyn "longship" had about 180 passengers on board.

"We were on our balcony, and we saw people in the water, screaming for help," said Ginger Brinton, a 66-year-old American tourist on the Sigyn.

"We never felt any bump. We didn't realise. We just saw people in the water. It was just terrible."

The tragedy comes five years after the Sewol disaster in South Korea in which more than 300 people, mostly children, perished when a ferry capsized in April 2014.

'Seven seconds to sink'

Security camera footage taken from a bridge "shows that before the collision the Mermaid turned towards the Viking Sigyn cruise boat, for some reason, the Viking then turned the small boat over, and it sank within seven seconds," police colonel Adrian Pal told a press conference.

The Mermaid was regularly serviced and had no apparent technical faults, Toth told Hungarian news agency MTI,.

Lee Sang-moo, chief operating officer of Seoul-based Very Good Tour company which organised the trip for the South Koreans, said most of the passengers were in their 50s and 60s, with the oldest a man in his early 70s.

Lee said 40 relatives are due to fly to Budapest from Friday, the same day South Korea's Foreign Minister Kang Kyung-wha is set to arrive along with a emergency task force.

Symptoms of hypothermia

Hungary's emergency services spokesman Pal Gyorfi said the seven rescued survivors were taken to hospital with symptoms of hypothermia and shock. Six of them were released Thursday, while one remained hospitalised with broken ribs, the M1 public television channel said.

The wreckage of the Mermaid was found on the riverbed near the Margaret Bridge, one of the main links between the two parts of the Hungarian capital, local media said.

A floating crane was erected near the accident site on Thursday, but experts warned that the Danube's high current level would make any diving attempts very risky and that lifting the wreck could take several days.

Zsolt Gabor Pataki, a colonel with the fire department, said the search operation had been extended to cover the entire length of the Danube in Hungary south of Budapest and that the authorities in neighbouring Serbia had been contacted.

In a phone call with Hungarian Prime Minister Viktor Orban, South Korean President Moon Jae-in called for "active support" from the Hungarian government in the rescue efforts.

Floral tributes and candles were left at the embassy on Thursday by locals expressing their condolences.

Orban sent a condolence letter to South Korean Prime Minister Lee Nak-yeon, and sought to ensure his counterpart that Hungary was making every possible effort to find survivors, Hungarian government spokesman Zoltan Kovacs said.

 The accident happened on a popular part of the Danube river for pleasure trips, from where passengers can view the city and parliament building illuminated at night.

Dozens of small sightseeing boats ply the river through Budapest every day. Larger river cruise boats travelling on the Danube between Germany and the Black Sea typically spend several days moored in the capital.