Auckland Mayor Wayne Brown is now suggesting a partial sale of the city's airport shares.
The council met on Thursday, with Auckland Council's Governing Body to reconvene on Friday morning.
In a statement, Mayor Wayne Brown said "this is a very hard budget".
"I want to ensure that we take our time to work through the process properly. I have always said it may take a couple of days of constructive debate. There is no issue with that, we are simply adjourning to another day," Brown said.
"While there remains some disagreement about the appropriate balance of levers, I am confident that we will finalise the budget before the statutory deadline of 30 June."
But a round table discussion at the meeting revealed Brown was unlikely to clinch the numbers for a full shares sale.
Instead, he's now proposing a sale of 8.09 percent of Auckland Council's airport shares, down from the 18 percent previously proposed.
The new proposal includes a general average rates increase of 7.7 percent.
Earlier, councillor Julie Fairey, the wife of under-fire Cabinet minister Michael Wood, was advised by the Auditor-General's office she didn't have a conflict of interest in regard to Thursday's vote on the sale of Auckland Airport shares.
Fellow councillors Wayne Walker and Chris Darby were also given the green light to vote.
Councillors were earlier asked to make sure they or their spouse didn't have any shares in the airport before partaking in the vote.
But earlier this week it was revealed Darby and Fairey held shares. Walker's shares were only brought to light on Thursday, hours ahead of the meeting.
Fairey's husband Wood was stood down as Transport Minister this week after earlier failing to declare his airport shares. Prime Minister Chris Hipkins revealed on Wednesday Wood was asked 12 times by the Cabinet office about selling them - but didn't.
"The shares my spouse holds - noting it's a very small shareholding - are in the process of being disposed of," Fairey told fellow councillors on Thursday.
"I have now received written advice from the office of the Auditor-General and from [the] council's legal team that, in their view, my situation does not represent a conflict of interest - as I cannot reasonably expect financial loss or gain from these decisions and that I am, therefore, able to participate under the Act.
"The budget votes today are the most significant decisions I have had the opportunity to vote on so far. To that end, I will be participating in the meeting on all items today."
Meanwhile, Brown earlier indicated "it may end up taking a couple of days" to reach an agreement on the city's budget.
"This is a difficult process and may take more time than expected," he said. "That's fine and we may even have to come back next week."
Council chief executive Jim Stabback said the budget required "compromise and difficult trade-off decisions.
"In this term we have seen a financial challenge like no other," Stabback said, singling out skyrocketing inflation and multiple storm events.
