According to the airline, forward bookings and demand continue to show a "positive increase" as a greater number of markets unlock and ease restrictions.
Last month, the carrier flew 225,509 passengers, which, according to Norwegian, is around 100% more than June 2020.
Compared with last year, the total capacity for June reportedly increased by 182% with passenger traffic up 102%.
Geir Karlsen, chief executive of Norwegian, said the airline has seen a continued month-on-month increase in bookings.
"June traffic results still show the impact of low demand due to reduced flying schedules and government imposed travel restrictions," he added.
"However, we have seen a continued month-on-month increase in bookings as countries ease restrictions.
"As a result, we have resumed flights to a number of key European destinations, we will continue to adjust and increase our network and schedules as demand rises."