Air New Zealand also offered direct flights to Bali over peak season but that would not, begin until June 15.
Brent Thomas, House of Travel commercial director, said the eruption had not interrupted customers' travels. "Typically, people can carry on with their holidays."
Thomas said safety was paramount for travellers, who were currently on "a 'watch and see' basis, particularly for many of those who arrived in Bali before the eruption.
"It could go dormant again or it could erupt again, no one knows".
Thomas' key advice for travellers was to have a chat with their travel agent and check Safe Travel, which would provide a good indication of travel risk.
Bali was the fastest growing travel destination over the past 18 months for bookings and departures from New Zealand, said Thomas.
"Flights offered direct from Air New Zealand and Emirates has opened this up even more.
"Based on the popularity of Bali and air capacity, it will continue to be key travel destination for Kiwis."
Bali's national disaster agency decided against raising the alert level as the spread of lava and incandescent rocks remained within the 4km exclusion zone around the crater.
Agung became active again in 2017 after more than a half century of slumber following a major eruption in 1963.