Former US President Barack Obama's third and final day in New Zealand

Former US president Barack Obama is believed to have left New Zealand, travelling to Australia in a private jet.

Obama's motorcade arrived at Auckland Airport soon after midday and a private Gulf Stream jet departed soon afterwards.

The former president left the Sofitel at the Viaduct hotel by motorcade after a brunch with Wahine Toa, a group of about 20 Maori women leaders this morning.

The jet taking Barack Obama to Sydney, on the tarmac at Auckland Airport. Photo / Dean Purcell

A small crowd of onlookers gathered hoping to catch a sight of Obama but were once again disappointed.

His motorcade left from an underground carpark and side entry and Obama could not be seen through the tinted windows.

Barack Obama's Crown limousine leaves the downtown Auckland hotel.

Obama will speak at an event in Sydney tonight and is due to meet with Australia's Prime Minister Malcolm Turnbull before heading to Tokyo tomorrow.

Obama spent two and a half days in New Zealand - playing golf in Northland with former PM Sir John Key, meeting PM Jacinda Ardern and holding a public speaking event for an audience of about 800.

A powhiri at Government House was the only event open to the media and there were almost no opportunities for the public to catch sight of him.

Dinner with Obama

Last night Obama captivated an Auckland crowd, with tales of his presidency, family life, New Zealand, women leaders - and the 55-45 call on the daring raid on Osama bin Laden.

In a 75-minute Q&A session with actor Sam Neill in front of an invite-only audience of 1000 people, Obama joked he was visiting New Zealand on a "scoping" mission for wife Michelle.

He had not visited New Zealand until now because the country was a true friend and ally that had never caused issues during his presidency. He was particularly praising of Sir John Key for his support, as a leader and friend, during their respective tenures.

One of his most revealing comments on leadership came around the raid on the Pakistan compound in 2011 and the killing of al Qaeda leader Osama bin Laden.

He explained that issues only arrived on the Oval Office desk if they "were not entirely solvable".

Sam Neill interviewed Barack Obama at last night's dinner. Photo / Dean Purcell

As an example, he said it was still only a 55-45 chance that bin Laden was in the compound and not, say, a Pakistan general. "Once you are in the situation, you have to take the lead."

The 44th president of the United States of America also shared insights about life after the presidency and the importance of women in leadership roles and around boardroom tables.

He said he wasn't joking: he firmly believed if every country had a female leader for a mandatory period of, say, two years, then issues such as war, conflict and child poverty would ease.

Obama was dressed in a steel-blue/grey suit, open neck white shirt and black shoes as he sat in a large sofa chair in front of guests including Key, Sir Peter Jackson, Willie Apiata, and Theresa Gattung.

Sam Neill joked to Obama that he'd only bought a tie earlier in the day - only to be told he wouldn't need it. Obama said ties were constraining and he now tried to avoid them unless it was for a wedding or funeral - or meeting the Queen, "who I love".