Rescuers looking for the missing are battling strong currents with Seoul requesting that the search be extended further south along the Danube.

"We have firmly decided that we won't give up our hopes about the possibility of finding survivors," South Korea's Foreign Minister Kang Kyung-wha told a news conference in Budapest.

Kyung-wha arrived in the city with an emergency task force and on Friday visited the site of the crash along with her Hungarian counterpart Peter Szijjarto.

Later in the day, officials escorted the relatives of victims, who had also arrived on Friday, to the riverbank.

The prospects of finding any more survivors are seen as very slim.

Only seven people are known to have survived so far. Those missing include a six-year-old girl and the boat's Hungarian captain and a crew member, while seven South Korean tourists are known to have died.

Police said Thursday they had detained the 64-year-old Ukrainian captain of the larger ship, the Viking Sigyn, for questioning "in relation to 'endangering waterborne traffic resulting in multiple deaths'".

The captain's lawyer, Balazs Toth, told Hungarian news agency MTI that his client, who had 44 years of experience "denied having committed a crime or not having respected all the rules".

"He has never caused an accident. He regrets he did not have the means to avoid the accident," he said.

The Viking Sigyn itself left Budapest with a new captain on Friday and reached the Hungarian city of Esztergom, according to local media.

Some survivors have described their terrifying ordeal as the Mermaid sank almost immediately and they were pitched into the dark waters.

Some were able to grab on to rescue buoys and watched in horror as fellow passengers struggled to stay afloat. 

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

The Mermaid is still completely submerged in the Danube, which has been swollen by weeks of rain.

A floating crane was erected near the accident site, as well as a small pier for use by divers.

But the strong current has made diving attempts very risky and complicated plans to lift the wreck.

Grainy images taken with sonar equipment showed the vessel on the bottom of the Danube, tilted to its side with its highest point two meters (6.6 feet) under the surface and its lowest 7.5 metres underneath, according to Hungarian news site index.hu.

Szijjarto said that "several hundred" members of the emergency service and the armed forces remained active in the search and rescue operation on Friday but admitted: "We have to say that circumstances are working against us."

About 20 South Korean divers have also arrived. But the water level is not expected to start receding before Tuesday.

Police have said the strong current swept one of the victims around 11 kilometers (seven miles) downstream of the accident site.

A candlelit vigil for the victims is expected at the South Korean embassy in Budapest on Friday evening.

Lee Sang-moo, chief operating officer of Very Good Tour which organized the trip for the South Koreans, said most of the Mermaid's passengers were in their 50s and 60s.

The youngest was the missing six-year-old girl who was travelling with her mother and grandparents and the oldest was a man in his early 70s.

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

Larger river cruise boats travelling on the Danube between Germany and the Black Sea typically spend several days moored in the capital.

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. (AFP)