Al-Attiya said Sunday the parliament reached a formula for the election law that was accepted by all the blocs.
Hill told CNN a vote will be held in Kirkuk, but that the election law will not solve the issue.
"Kirkuk will be solved by a political process which involves the good offices of the U.N.," Hill said.
Another key dispute holding up the law has involved lists to be used on election day.
Politicians disagree over whether to use open lists that name candidates or closed lists that name just their parties. The law used in the 2005 election calls for a closed list. The law that passed Sunday calls for open lists.
Al-Maliki called the use of open lists part of the "historic victory."