In a searing critique of Israeli policies published on Friday in The Guardian newspaper, Livingstone also rejected calls for an apology for comments made last month comparing a Jewish reporter to a concentration camp guard.
Sharon "is a war criminal who should be in prison, not in office", he wrote, saying that even an Israeli commission had blamed the prime minister for massacres at Palestinian refugee camps in Lebanon.
The mayor also denounced "ethnic cleansing" of Palestinians during the expansion of the Israeli state, Israeli settlements in the occupied territories and the denial of Palestinians' right to return.
"Sharon continues to organise terror," he said, citing the disproportionate number of Palestinians killed compared to Israelis during the Palestinian intifada or uprising.
Rejecting charges of anti-Semitism, Livingstone argued it was necessary to separate criticism of Israeli policies from anti-Semitism, saying the Israeli government deliberately attempted to conflate the two.
Livingstone said Sharon should be
in jail, not in office
The Israeli government has for the past 20 years "attempted to portray anyone who forcefully criticise the policies of Israel as anti-Semitic. The truth is the opposite: The same universal human values that recognise the Holocaust as the greatest racist crime of the 20th century require condemnation of the policies of successive Israeli governments", he wrote.
Livingstone's comments were in response to criticism printed a day earlier in the newspaper by the head of the Board of Deputies of British Jews, Henry Grunwald.
Last month, Livingston had compared Oliver Finegold, a reporter for the Evening Standard, to a concentration camp guard.
But the Labour mayor rejected a fresh call for an apology.
"No serious commentator has argued that my comments ... were anti-Semitic," Livingstone wrote.
His administration had fought anti-Semitism "tooth and nail" and he continued to "detest racism", he argued.