Baghdad, Iraq (CNN) -- U.S. Ambassador to Iraq Christopher Hill said Sunday that American officials were extremely relieved that Iraq's parliament passed a long-awaited election law.
Both the U.S. and Iraqi governments insist that this will allow national elections to take place in January.
"Whenever you're working on something like that and, you know, you're not really sure if it's going to be successful, you worry, you worry about it until it's actually done," said Hill, who spent a lot of time at Iraq's Parliament in the past two weeks, talking to elected officials and trying to ensure that the voting law was passed.
"I worried about it until I actually saw the votes in the parliament and I realized it was done," Hill said. "As someone who's seen a lot these things over the course of my career, it was kind of nice, kind of gratifying to see this real effort at democratic procedure."
The law has been the focus of great international concern, with United Nations and U.S. officials calling on Iraqi leaders to pass it.
It was also widely seen as a test of Iraq's ability to form a functioning government.
According to Hill, the biggest roadblock to passing the law had been the question of how balloting should unfold in the ethnically diverse and oil-rich province of Kirkuk, where Kurds displaced under Saddam Hussein's rule have returned to claim back their land. That has resulted in a power struggle among Kurds, Arabs and Turkmens.
Hill said a vote would take place in Kirkuk.
"I think everyone felt strongly that people in Kirkuk should be able to vote in these parliamentary elections. So, indeed, that's going to happen," he said.
"But it got really complicated when you tried to figure out, for example, which voter lists were going to be used," Hill said, "because some people felt that if you used this newer voter list, that somehow this would encroach on the issue of how you would eventually solve Kirkuk politically.
"So the law made very clear Kirkuk is not going to be solved in this election. Kirkuk will be solved by a political process which involves the good offices of the U.N."
Kurds have long regarded Kirkuk -- the province and the city of the same name -- as an integral part of Kurdistan, and many want it to be part of Iraq's autonomous Kurdish region. Arabs and Turkmens also lay claim to the city and province, and all the groups want their voices and votes to be adequately represented in the political system.
Tensions among Kurdish politicians and U.S. officials were so high at one point last week that a senior Kurdish lawmaker said the U.S. should stop interfering.
After Vice President Joseph Biden placed calls to Kurdish leaders pushing them to accept a compromise on the election law, Mahmoud Othman, a prominent Kurdish member of parliament, said U.S. officials, including those at the Embassy in Baghdad, were being "counterproductive."
Hill said that he was only trying to be helpful and that he thinks the help from the U.S. was well received.
"I wasn't trying to impose any solution. I wasn't wagging my finger and lecturing people about anything. I was trying to be helpful," Hill said.
Another key dispute holding up the law involved those lists to be used on election day. Politicians disagreed 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.
Most worrisome to U.S. officials in the leadup to the vote was the fact that any delay to Iraq's elections could cause Iraq's government to lose legitimacy, an outcome that might lead to a shift in the U.S. troop drawdown schedule.
Hill is confident that elections will take place by their constitutionally mandated deadline and that there will be no delay to the withdrawal timeline of the troops.
"We believe that we're in good shape for January and what was important was to have the U.N. technical people there throughout," Hill said. "Because as people were making changes, as I mentioned, even pen and ink changes, the U.N. people needed to be there to make sure these were technically feasible. And of course we have this Independent Election Commission, they work very closely with the U.N., so the belief is that we have a good piece of legislation which will enable this to go forward in January and that we will be on time."
CNN's Jomana Karadsheh contributed to this report.