Police in the Swiss city, which is home to the U.N. European headquarters and to many Tamil immigrants, said 200 buses from across Europe were expected to bring protesters in.
Demonstrators were expected to wind through Geneva in the afternoon and then rally in the public square in front of the U.N.'s Palais des Nations complex, where Tamils held smaller protests in past weeks as fighting intensified in Sri Lanka.
A Tamil man in his mid-20s killed himself by pouring gasoline on his body and setting himself alight during one demonstration last week.
One organiser said at least 10,000 Tamils were travelling from Britain, joining others from Switzerland, Germany, France, Norway and the Netherlands.
U.N. staff in Geneva said they had been told to go home from mid-day. Security was being tightened at the Palais des Nations, where 1,600 people work, a U.N. statement said.
The Liberation Tigers of Tamil Eelam (LTTE) rebels have fought for a quarter century for an independent homeland in Sri Lanka's northeast, but an army offensive has now cornered them in a small wedge of jungle.
The government formally abandoned a six-year-old Norwegian- brokered ceasefire a year ago.
John Holmes, the top U.N. humanitarian official, urged rebels and the government on Thursday to protect civilians. Around 36,000 have fled the war zone to government-run camps.
