Hopes have faded that any of the 21 people missing will be found alive. Pal says a criminal investigation has been opened into the incident.
Mihaly Toth, a spokesman for the Panorama Deck boating company, said the "Hableany" was on a "routine city sightseeing trip" when the accident happened.
"We know nothing about how it happened, the authorities are investigating, all we know is that it sank quickly", he said.
"The footage 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.
He added: "We never felt any bump". "We are with the victims and their families in our thoughts and prayers in these most hard times", Orban said, according to his spokesman.
No-one on the Swiss-registered Viking Sigyn was injured. Authorities said both vessels' captains are experienced, with many years of service with their companies.
What is known about the rescue operation?
A map released by Hungarian police showed the locations and times the seven bodies were recovered, with one body found almost 12 kilometres downstream, almost 21/2 hours after the collision.
"The boat flipped instantly and capsized", said Yoon, who had been travelling with her mother.
A massive rescue effort is now under way with boats, divers, spotlights, and radars all scanning the river.
"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.
It said the tourists were not wearing life jackets.
Budapest has enjoyed a boom in overseas tourism in recent years.
"A further 21 people are missing", a Hungarian police spokesman Kristof Gal told AFP.
What has the reaction been?
A team of South Korean officials will go to Hungary to assist with the rescue operation and support passengers and their families. "Foreign minister Kang Kyung-hwa will head an interagency task force and travel to Hungary".
'Music Bank' has been canceled this week due to the tragedy in Budapest.
Thirty-fivepeople - including 33 South Koreans - were on board the boat when it collided with another vessel in theHungarian capital Wednesday night, according to South Korean's Ministry of Foreign Affairs (MOFA). The craft had been carrying a South Korean tour group.
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