Mr Livingstone said that any violence at the protests would not be "incidental".
He said people who came with the intention of engaging in criminal activity should be arrested and charged without unnecessary delay.
On the same day last year, protestors dug up Parliament Square and daubed statues with graffiti and attacked business premises.
Protecting tourism
Mr Livingstone said: "I support the cancellation of Third World debt and the eradication of poverty, oppose the privatisation of the Tube and want to defend the environment against pollution.
"But these demonstrations will set back these causes.
"I want to urge everyone who has the slightest sympathy with any of the stated objectives of the protesters not to attend this action on 1 May."
Mr Livingstone said that any violence at the protests would not be "incidental".
He said that as mayor it was his duty to look after London as a whole and that included protecting the tourism industry.
"London's economy has already been badly hit by the impact of foot-and-mouth and turning major tourism and shopping areas into economic targets is simply not acceptable."
Getting tough
He added: "Anyone whose intention it is to engage in criminal activities should be arrested and charged without prevarication or unnecessary delay."
Mr Livingstone's strong condemnation is being contrasted to his stance last year when he told an interviewer that he had always backed "direct action".
His response drew stinging criticism from politicians who urged him to condemn rioters.
Mr Livingstone, rejected allegations that he had supported the 1999 City of London riots, and later branded the demonstrators as "mindless thugs".
Metropolitan Police Commissioner Sir John Stevens believes that this year some anarchist groups are using the internet to plot their campaign.
In February he said: "There are strong indications to suggest that planning by protest groups is well advanced and that their intention is to disrupt the everyday workings of London life."
The mayor is due to be briefed by Metropolitan Police Commander Michael Messinger on Wednesday.
Last year, violence flared as some demonstrators daubed graffiti on the Cenotaph in Whitehall and then clashed with police in Trafalgar Square.
They also vandalised the statue of Winston Churchill in Parliament Square.