"This (the bill) will give our Western partners the ability to put pressure on Russia to fulfil three basic points of the Minsk agreement - the ceasefire, withdrawal of Russian forces from Ukraine and re-establishment of control over the border," said Maksim Burbak of Prime Minister Arseny Yatseniuk's Popular Front party.
"We have to support the international 'anti-Putin' coalition," said Yuri Lutsenko of the Poroshenko bloc, referring to Russian President Vladimir Putin.
But opponents of the bill said it played into Russia's hands and would lead ultimately to Ukraine losing control over the Donbass - the name given to the industrialised east, swathes of which are controlled by separatists now.
"We believe that these anti-Ukrainian changes to the Constitution ... are a road to realisation of Putin's plan for destroying Ukraine," said Radical party leader Oleh Lyashko.
"This is not the road to peace but to decentralisation. This is a diametrically opposed process which forces us to lose territory," said Tymoshenko.
"Putin does not need the Donbass. He needs war in Ukraine. Our task in the vote is to get back to negotiations on the right road to bring peace, not the illusion of peace," she said.
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A Reuters TV cameraman said police were knocked off their feet by the blast of the explosive device - assumed to be a grenade - thrown from the crowd. He said two police were treated for wounds at the spot and there were pools of blood on the street.