Writing on Twitter, Mr McGuinness said people should "resist celebrating the death of Margaret Thatcher".
The Deputy First Minister added: "She was not a peacemaker but it is a mistake to allow her death to poison our minds."
But despite his pleas, huge crowds gathered at the Falls Road in west Belfast tonight following Ms Thatcher's death on Monday.
Young children and adults brandished Tricolour flags along with images of hunger striker Bobby Sands.
A raft of of cars left the Twinbrook Estate - former home of Bobby Sands - and made its way to Divis Tower close to Belfast City Centre.
Meanwhile a crowd of two or three hundred people assembled in Glasgow's George Square yesterday where in 1989 protests to the introduction of Thatcher's poll tax took place.
Some wore party hats and launched streamers into the air while a bottle of champagne was opened with a toast to the demise of Baroness Thatcher.
Members of various organisations including the Anti-Bedroom Tax Federation, the Communist Party, the Socialist Party, the Socialist Working Party, the International Socialist Group, were joined by members of the public to mark the occasion.
More than 100 people gathered in Brixton, south London - the scene of fierce riots in 1981 - two years into her first time in office.
In Northern Ireland a crowd gathered in Londonderry to 'celebrate' the death. Many waving Tricolour flags gathered at the famous Free Derry Corner in the city's Bogside.
Several Chinese lanterns were lit as families gathered in the area. Crowds also gathered on the Falls Road in west Belfast on Tuesday.
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