Labour Minister Faruk Celik said that the governments position remained unchanged, despite pressure from unions.
The governments view on the issue is quite clear for the moment and there is no shift in our assessments about the May Day celebrations and about the Taksim square, said Celik.
May Day celebrations at Taksim square have been banned since 1977, when gunmen opened fire on demonstrators, killing 37 people and wounding dozens of others.
No one has ever been charged over the shootings.
Earlier Tuesday, Prime Minister Recep Tayyip Erdogan met with the leaders of Turkeys major trade unions to discuss their demands to be allowed to hold a May 1 rally in Taksim.
However, Erdogan made it clear that May Day activities in Taksim would be strictly limited.
Trade union representatives can lay a wrath at the Ataturk monument in Taksim Square and make a press statement, Erdogan said.