The 48-year-old, who will stand unopposed for re-election in May, also met Trade Minister David Parker and was earlier welcomed by a haka and local junior team.
The principal purpose of Infantino's visit was to attend yesterday's OFC Extraordinary Congress, which saw Lambert Matlock (Vanuatu) confirmed as president and New Zealander Johanna Wood elected to the 37-strong Fifa Council.
OFC is rebuilding after the turbulent, autocratic reign of former president David Chung, who resigned last year amid fraud claims related to the new headquarters in East Auckland, where millions of dollars of Fifa money remain unaccounted for.
Chung was suspended from football for six years for conflicts of interest and accepting and offering gifts, and Infantino warned OFC must continue to reform.
"If there is still someone who is involved in football in Oceania who has not realised yet that the times of abusing football for personal gain is over, then we really cannot help any more," said Infantino.
"This is the last opportunity for Oceania. Now we can focus on football. The past is over."
Infantino remains hopeful of a 48-team World Cup in three years, despite logistical challenges in the Gulf.
"It is good for football to increase the number of participating teams," said Infantino. "If we don't give a real chance to many countries in the world to participate, we don't really do our job. You [currently] have half a slot in Oceania. If you are drawn against No 5 in South America, it is very, very difficult to qualify.
"If you increase the number of teams, you increase the number of slots, you increase participation and you increase investment. We are working on it. If it happens, great. If it doesn't happen, we tried."
Infantino is also a strong advocate of a quadrennial Club World Cup with 24 teams to replace the current annual seven-club event.
"The problem is nobody knows about it," said Infantino. "And why nobody knows about it? Because the current Club World Cup is not good.
"And it has to be changed to have a real impact, with maybe 24 teams, of which at least one should be from Oceania — one fixed spot, not a half spot.
"In a real Club World Cup, in June, the best teams of the world will participate, including one from Oceania. This will boost club football all around the world and particularly in Oceania."