British police said they believed British-born 22-year-old Salman Abedi carried out the bombing that killed 22 people following a concert by American pop singer Ariana Grande in Manchester on Monday and have raised their threat level to "critical".
The Lions arrive for their 10-match rugby tour next week and, with memories of a similar 2015 attack in Paris that targeted numerous venues including the Stade de France during an international soccer match, English said officials in New Zealand were being cautious.
"Intelligence agencies are always monitoring for these kinds of attacks," English told reporters at New Zealand's Parliament Buildings on Wednesday.
"The risks of an attack are monitored constantly, we have a strong focus on public safety.
"There is no evidence of heightened risk of attack in New Zealand or around the Lions tour, but we will remain vigilant."
The Lions begin their tour in Whangarei on June 3 against an invitational Provincial Barbarians selection. The first test against the All Blacks is on June 24 in Auckland before the tour concludes on July 8 with the third test.
(Writing by Greg Stutchbury; Editing by Peter Rutherford)
