At least seven people were killed and nearly 20 were missing after a pleasure boat carrying South Korean tourists capsized on the flooding Danube in the Hungarian capital on Wednesday, police and ambulance officials said.

The boat reportedly collided with another tourist vessel near the Hungarian parliament building, before turning over on the river, which has been flooding, with very strong currents, while a rainstorm enveloped Budapest.

In Seoul, the foreign ministry said the South Koreans aboard the vessel when it sank were 30 tourists and three tour guides, in addition to the crew of two Hungarians. Seven of the South Koreans were rescued, seven died and 19 were missing, it added.

"South Korean President Moon Jae-in issued an urgent order to work with the Hungarian government for rescue efforts," his spokeswoman, Ko Min-jung, told reporters.

An emergency rescue team is among the 18 officials South Korea is sending to Budapest, the foreign ministry added, and it will provide counselling to victims' families.

A Hungarian ambulance spokesman told state television that 14 people were pulled from the water. Seven have died, with the rest suffering from hypothermia but stable.

A massive rescue effort deployed boats, divers, spotlights, and radar scanning to scour the river for several kilometres downstream from the accident site.

Journalists at the scene said they saw children's ambulances on the riverbank.

There was a six-year-old on board, said Lee Sang-moo, an official of the South Korean travel agency that booked the group tour. But the child did not figure on the list of survivors, the agency added.

The hours that have passed since the accident, soon after 9:00pm (1900 GMT), make it less likely for new survivors to be found in the central Budapest area, as strong currents have carried people far downstream, emergency rescue chiefs told state media.

The National Ambulance Service mounted searches along a stretch of the river downstream from Budapest and was on alert along a section further south in Hungary, where all boat traffic has been halted.

Television images showed the bank of the Danube closed off by police on the Pest side, across from the World Heritage site of Buda Castle.

The Danube's flooding and currents made rescue efforts extremely difficult, a rescue diver told the state broadcaster, with water temperatures ranging between 10 and 12 degrees Celsius (50 and 54 degrees F).

The boat, the Mermaid, was a 27-m (89-ft) double-decker river cruise boat with a 150-horsepower engine and could hold up to 60 people, its owner, Panorama Deck Ltd, told state media.

"We are mobilising every resource we have to protect human lives," it said, adding that the Mermaid had been in its fleet since 2003, with regular maintenance.

Boat registry Hajoregiszter.hu showed the ship, originally built in the Soviet Union in 1949, received a Hungarian-made new engine in the 1980s.

Neither the registry nor the operator could be immediately reached for comment on the boat's age.

A shipping expert told state television it was likely the pleasure boat had collided with a very large vessel that had sunk it very quickly.

The hull was found on the riverbed just a few hundred metres from its usual mooring point.

In 2014, South Korea grappled with a shipping disaster that involved schoolchildren, who made up a large portion of the 300 people killed in the Sewol ferry sinking.