* Two bodies found, in sunken boat and 60 km downstream
* Conditions improving, salvage crane expected on site
* Goal is to bring ship to surface as waters recede (Adds bullets, two more bodies found)
By Marton Dunai and Hyonhee Shin
BUDAPEST, June 4 (Reuters) - The South Korean government expects to begin returning to Seoul the remains of some of the victims who died last week when a tourist boat sank in Budapest, an official said on Tuesday, as conditions for exploring the wreckage improved.
Twenty-eight people are presumed to have died when The Mermaid, a pleasure boat carrying 33 South Korean tourists and two Hungarian crew, capsized and sank after being hit by a cruise liner in Budapest last Wednesday.
Seven Koreans survived and another 17 people are listed as missing after divers freed a body from the wreck's window and brought it to the surface on Tuesday, with another body pulled from the river 60 kilometres (37 miles) downstream.
While the second body is still being identified, assuming it is from the wreck the confirmed death toll now stands at 11.
"During their morning dive Hungarian divers found a body in the window of the wreckage," the counter-terrorism centre TEK, which coordinates emergency responses, said in a statement, adding that strong currents and zero visibility made recovery exceedingly difficult.
"It took preparation and a six-hour strenuous team effort to bring the body to the surface in the afternoon," it said, adding that the primary goal of the teams was to salvage the ship from the riverbed.
The search has extended hundreds of kilometres south, into Serbia, as some bodies have floated downstream. South Korea has asked Hungary to reinforce the search around Harta, where the body was found on Monday, Korean Embassy Defense Attache Song Shun-keun said.
The Danube's flooding has hampered recovery work, officials said, but waters are now receding.
"The operational environment continues to improve," Song told a news briefing. "But we are still struggling to get into the ship due to bad visibility."
Korean Deputy Foreign Minister for consular affairs Lee Sang-jin, who is in Budapest to lead the emergency response team, said he expected soon to be able to start returning to South Korea the bodies already identified.
If they are willing, survivors may speak to Hungarian investigators later on Tuesday, Lee added.
South Korean and Hungarian rescue and recovery teams have set up bases on the river and on the nearby Margaret Island, within sight of the crash site. They might mobilize drones if visibility improves, the attache said.
Song said he expected salvaging the vessel to begin on Thursday, after a crane has been delivered, adding that work could begin on Friday or Saturday.
South Korea has asked Hungary to ensure that the captain of the cruiser, a 64-year-old Ukrainian under arrest pending bail, is not released. His lawyers said the captain was devastated by the accident but had done nothing wrong. (Additional reporting by Reuters staffers in BUDAPEST and SEOUL, Editing by Larry King and Gareth Jones)