Candidates have three days from the public notice being published this Saturday to seek a judicial recount.
Southgate was not yet prepared to concede to King on the basis of the preliminary results.
"It's incredibly tight and all credit to Andrew King for running a good race," she said.
"He's run a strong campaign, so congratulations to him and we will wait and see what the final results are."
Despite the narrow margin indicating he was in front for the race to the mayoralty, even King wasn't ready to say the job was his.
"It's definitely not a done deal," he said. "I'd imagine this is going to go on for several days."
But despite the "cliffhanger" of a race, King said he wasn't too worried.
"I'm just quietly waiting, not uptight or stressed at all," he said. "I just find it very exciting."
King said it was never certain he'd be the one the people would choose to lead the city through the next term.
"At the end of the day it's the people who have voted and it's the people who have chosen," he said. "I knew it was always a four-way race - it could have gone any of four ways - but it's obviously down to two."
King said he'd heard from Rob Pascoe and Chris Simpson, the other two main contenders in the race.
"They were just acknowledging they were out of the race," he said. "Very gracious phone calls."
Until the final votes were counted King said he'd be just "going on with my life as normal".
Electoral officer Dale Ofsoske could not recall a tighter mayoral race in recent years, although he said there had been a draw for the Great Barrier Local Board in 2013 and a policeman ended up drawing the name out of a hat to decide the successful candidate.
In 2010, Celia Wade-Brown beat incumbent mayor Kerry Prendergast by 176 votes, which was the closest margin seen in the Wellington mayoral race.
The same year newcomer Julie Hardaker beat incumbent Bob Simcock by 956 votes to become Hamilton mayor.
Meanwhile Waikato DHB members were confirmed last night with former Waikato DHB communications director Mary Anne Gill and Hamilton City Councillor Dave Macpherson the two newcomers.
Macpherson, whose son Nicky Steven died while in the Waikato DHB's Henry Bennett Centre's care in March last year, said the appointment was "bitter-sweet".
While he would not have thought of standing if it had not been for the death of his son, he said he was not there to seek revenge but to ensure improvements were made.
Martin Gallagher, Pippa Mahood, Crystal Beavis, Clyde Wade and Sally Christie held onto their seats. Andrew Buckley was not re-elected.