At least 6,000 Europeans are still missing - most of them presumed dead - after the Indian Ocean disaster wrecked beach resorts in south-west Thailand.
Aid workers in Phuket are trying to trace the missing
Sweden estimated 3,500 of its people were missing and said the national death toll could top 1,000.
Germany has more than 1,000 missing, and hundreds of tourists from Italy, Norway, Denmark, Finland and the Netherlands are also unaccounted for.
The Thai resorts of Khao Lak and Phuket were hardest hit by the giant waves.
Nearly 2,000 foreign tourists died in Khao Lak alone, when luxury hotels full for the Christmas holidays were swamped.
Bodies arriving in temporary mortuaries are often unrecognisable after days lying in the tropical heat.
More than 4,500 bodies have now been recovered in Thailand, almost half of them foreigners.
EUROPEANS DEAD OR MISSING
Sweden: 59 dead, about 3,500 missing
Germany: 34 dead, over 1,000 missing
Britain: 34 dead, unconfirmed number missing
France: 22 dead, 96 missing
Norway: 21 dead, 430 missing
Italy: 14 dead, 700 missing
Finland: 14 dead, 263 missing
Switzerland: 12 dead, 850 missing
Denmark: 7 dead, 419 missing
Austria: 5 dead, up to 100 missing
Russia: 1 dead, 80 missing
Where possible, the bodies of foreign tourists are being stored in refrigerated container lorries, but more temporary mortuaries are needed to house corpses.
Forensic experts will try to identify victims using DNA samples and dental records provided by relatives.
The highest death tolls confirmed by European nations so far are: Sweden (59), Britain (34), Germany (34), France (22) and Norway (21).
The actual death tolls are expected to be much higher.
Sad New Year
New Year's Day will be an official day of mourning in Sweden, Finland and Norway.
Many local authorities throughout the Nordic countries have cancelled New Year celebrations.
European countries have pledged millions of dollars in aid and planes carrying experts and supplies have been flown to the region.
The EU's humanitarian affairs commissioner, Louis Michel, said the EU had reserve funds to help the stricken countries if the 33m euros ($45m) already pledged proved insufficient. He said the EU had an extra 300m euros available in separate emergency funds.
But he stressed that funds would be needed for reconstruction, beyond the current emergency.
On the ground in the disaster zone, many Europeans are still waiting for news of friends and relatives missing since Sunday's waves.
Locals and tourists are looking at the dead to see if their loved ones are there, or examining message boards posted with photos of the dead.
One of the coordinators of the forensic teams in Thailand, policeman Carl Kent from Australia, urged relatives to refrain from visiting the mortuaries, which were in "difficult environments".
"Family members must steel themselves to the fact that this process will take a considerable period of time to resolve," he said.
The BBC's Chris Hogg in Phuket says that after the Bali bombing it took five months to identify about 200 victims.
The Danish, Swedish and Norwegian foreign ministries have been sharply criticised by some of their nationals in Thailand, who accuse them of reacting too slowly to the disaster.
The European Union is planning a special meeting of EU aid ministers early next month to co-ordinate relief efforts.
Mr Michel said he would attend a conference of the Association of South-East Asian Nations (Asean) in Jakarta next week to gauge the immediate needs.