The Swiss government has promised an additional SFr25 million ($22 million) in immediate aid to countries hit by the tidal waves in southeast Asia.
On Thursday, the foreign ministry said it feared a "huge increase" in the number of Swiss victims.
The SFr25 million comes on top of the SFr1 million pledged as news of the disaster broke on Sunday.
“The terrible earthquake on December 26 has shaken us all to the core,” Deiss told a news conference in Bern.
Deiss said the extent of the devastation meant that it could only be effectively tackled if all countries worked together. He said Switzerland was prepared to host a donors’ conference in the first half of January.
Toni Frisch of the Swiss Humanitarian Aid Unit said reconstruction would take generations.
Switzerland has sent five experts to Indonesia and two others to the Maldives. Swiss teams are already active in India, Sri Lanka and Thailand.
On Thursday, 22 Swiss pathologists arrived in the Thai resort of Phuket to help with the identification of bodies. They are expected to remain at the scene for up to two weeks.
Sunday's disaster has claimed the lives of more than 130,000 people in coastal areas of southeast Asia.
Twelve Swiss have now been confirmed dead in the tidal waves, and a further 850 are still missing.
The foreign ministry said it feared the number of Swiss dead would increase dramatically over the coming days.
"We fear a considerable, even huge, increase in the number of [Swiss] victims," said Peter Sutter of the foreign ministry crisis management unit.
Swiss Solidarity, the fundraising arm of the Swiss Broadcasting Corporation, said on Thursday that it had already collected SFr11 million ($9.7 million) in donations.
Meanwhile, the Swiss Air Rescue Service has announced it is sending a third air ambulance to Phuket. The first jet returned to Zurich with five injured Swiss late on Wednesday.
A nationwide fundraising day for the victims of the natural disaster is due to take place on January 5. An interdenominational memorial service will be held in Bern cathedral on the same day.
Deiss said he would be attending the event, along with the 2005 Swiss president, Samuel Schmid, and Foreign Minister Micheline Calmy-Rey.
swissinfo with agencies
Switzerland initially pledged SFr1 million in aid to quake victims.
On Thursday, it announced it was giving a further SFr25 million.
Switzerland is expecting to play a role in reconstruction in the affected region and has proposed a donors' conference.
A memorial service will be held on January 5 in Bern cathedral.
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