A separate group from Tonga were in Christchurch and have now travelled to Auckland.
Inspector Sam Aberahama, the Tairawhiti area commander, wouldn't comment on speculation the bus's brakes failed, saying "we need to get the bus out before we can speculate any further on that".
The ministers have been to the accident site and were at a vigil at the Wesleyan Methodist Church in Gisborne on the evening of Christmas Day.
They have visited survivors in Gisborne Hospital and let them use their phones to call home.
They believe the Tongan community is reassured by their presence among them so soon after a tragedy.
"We had a Tongan hymn and song to acknowledge the occasion - that was a cultural part for us to conduct that at the time," Mr Ngaro said of the visit to the accident site.
Mr Sovaleni said the key concern now was getting the passengers back to Auckland and back to Tonga.
On Monday, police said crowds heading to the Rhythm and Vines event were advised that SH2 between Wairoa and Gisborne was open and will be open on Tuesday but will shut at some point during the next two days to retrieve the bus.
New Zealand's holiday road toll currently sits at eight.
Last year, there were 12 deaths on the roads during the holiday period. This year the holiday period runs from 4pm on December 23 to 6am on January 4.
- AAP
