Kosova: Serbia Claims Sovereignty
The move, passed during a special session of parliament, opposes calls for the ethnic Albanian majority in Kosovo to be given independence.
Kosovo has been run by the UN since Nato intervened in 1999 to stop
The proposed constitution will now face a referendum before it becomes valid.
Mr Kostunica said the country's new constitution would "cement the truth that Kosovo always has been and always will be an integral part of
He also insisted there was no need to wait for the Kosovo issue to be settled before adopting the new constitution.
The BBC's Nick Hawton says this is a controversial statement, as negotiations on the province's final status are currently under way.