The threat to fight the bill in Iraq's national parliament comes just days after the oil ministry in Baghdad warned regions against signing contracts until the law was passed.
Officials from the Iraqi government and Kurdistan have clashed over the annexes, raising the prospect of delays that have already dogged the lengthy drafting of the legislation.
Hawrami repeated a threat that his oil-rich region would implement its own oil laws if no agreement was reached on the dispute over the annexes.
And Kurdish officials have already signed deals with foreign oil companies.
"The annexes must recognise that the Kurdish regional government has already allocated exploration and development blocks in the Kurdistan region under Production Sharing Agreements pursuant to the Iraq Constitution," he said.
In a reference to Saddam Hussein, Hawrami said the newly created Iraq National Oil Company (INOC) would be a return to "old regime methods".
"The concentration of power in the hands of INOC will represent a return to method of petroleum management of previous Iraqi regimes.
"Where centralised oil power was ... used to fund violent campaigns by elites against neighbouring countries and against our own Iraqi citizens," he said.
Officials from the central government and Kurdish regional officials have said they would meet to settle the disputes, but Hawrami said sending a delegation to Baghdad was "futile".
A US government official in Baghdad said on Sunday Washington was confident the law would pass.
"I think that the government is committed to getting the oil law through. I know various bodies have expressed concern about the hydrocarbon law given the stakes involved," the official said.
"The government has a majority in parliament."