While there were no sign of impacts craters or blocks beyond the main crater area, visitors were now faced with the highest level of risk since the end of the 2001 eruptions, he said.
Mr Scott said additional hazards to visitors to the island included the health effects of volcanic ash and acid gas exposure, including respiratory issues, skin and eye sensitivity.
More explosive eruptions could occur at any time with little or no warning, he said.
"We continue to monitor the volcano and advise a high level of caution should be taken, if visiting the island," he said.
During the past fortnight there had been an increase in volcanic tremors, volcanic gas levels and the crater lake water level on White Island rose 3m to 5m.
The alert level has been raised from one to two on a scale of zero-five where as White Island in the past had consistently sat at alert level one.
Mr Scott said the last time White Island erupted, it continued to be active for 25 years, from 1975 to 2001, and no one knew whether it was the start of another 25 years of activity.
But Mr Scott said the recent volcanic activity on White Island, and the Mt Tongariro eruption on Monday night were unrelated.
"Every volcano is an individual in terms of its volcanic system and it's coincidental that they are both active at the same time," he said.
Mr Scott said both volcanoes may share the same plate boundaries, but each volcano was independent of the other.
GNS Science are also continuing to monitor seismic activity on Mt Tongariro which had not blown since 1897, and has not erupted again since Monday's steam-powered eruption. Seismic activity at Mt Tongariro is currently assessed as low level.