Irene Khan, Amnesty's secretary general, visited Brussels on Tuesday to meet with European Union officials to discuss the report.
However, she stopped short of supporting calls for a boycott of the Olympic Games over the issue which China will host in August.
Khan said she did not want a boycott but said other groups should use their influence on China through their participation in the games.
She said: "What we are calling for is that those that have some influence, that is the Olympic Committee itself, corporate sponsors and governments, should use that influence to get China to keep the promises that it made [in order to secure the Beijing Olympics]."
Piers Bannister, an Amnesty researcher, said: "I hope, as China takes its place on the global stage, that it will seriously look at its human rights record, and that one of the things it will do is abolish the death penalty."
Noting that Beijing classifies the death penalty as a state secret, Amnesty said that "as the world and Olympic guests are left guessing, only the Chinese authorities know exactly how many people have been killed with state authorisation."
Khan said: "We've seen human rights abuses intensifying in the lead-up to the Olympics, [with] a crackdown on activists and the use of re-education labour camps in lieu of detention."
'Veil of secrecy'
The Amnesty report said 88 per cent of all known executions take place in just five countries, China, Iran, Saudi Arabia, Pakistan and the United States.
It said Iran carried out at least 377 executions, while the figure for the United States was 42.
The organisation called on all governments that allow the death penalty to lift what it called the "veil of secrecy" over the practice.
Bannister said: "We need to see that the borders of execution-free Europe and the Americas are pushed back into the Middle East and Asia until we see a world free of executions."
China's hopes of winning international prestige by sending the Olympic torch through 135 cities on five continents ahead of the games have already been severely dented.
The early stages in London and Paris were overshadowed by demonstrations against Beijing's repression of protests in Tibet, and the San Francisco leg was also drastically curtailed and seen by relatively few people.
Angela Merkel, Germany's chancellor, has already vowed to boycott the opening ceremony of the games and several other countries are considering the same action.