Trump initially declared he was "not happy" with the missile tests carried out on May 4 and 9 but then played down their importance by calling them "standard stuff".
"In terms of violating Security Council resolutions, there is no doubt about that," Bolton told reporters in Tokyo in advance of the US President's four-day visit to Japan.
"I think the Prime Minister and President are going to talk about making sure the integrity of the Security Council resolutions are maintained," he said, referring to a Monday summit meeting between Japanese Prime Minister Shinzo Abe and Trump.
It is the first time that a high official in Trump's administration described the North Korean tests as violating UN sanctions. Until now, both South Korea and the US downplayed the launches, which were supervised by North Korean leader Kim Jong-un.
Bolton said that Washington fully supports efforts by the Japanese Prime Minister to meet with Kim without any preconditions, the New York Times reported.
According to him, the President already had "two unconditional meetings with Kim Jong-un" in Singapore and Hanoi and that he did not see "anything untoward" in Abe pursuing a similar meeting with the North Korean leader.
Bolton said the US had not heard much from North Korea since the Vietnam summit in February, which ended abruptly after Trump rejected Kim's suggestion that Washington lift the most painful of sanctions imposed on his country since 2016 in exchange for a partial dismantlement of its nuclear weapons programme.
"We really have not heard much from North Korea since the Hanoi summit," he said, adding that US officials were "ready to have further discussions at the working level to see what progress might be made".
The US National Security Advisor said that Trump's special envoy for North Korea Stephen Biegun, "can't wait to talk to his North Korean counterpart but they have not responded".
"He is ready at any point to get on a plane and go anywhere to talk to them," he added.
During his Japan visit, Trump will hold meetings with Abe starting Sunday and meet Emperor Naruhito on Monday.
( With inputs from IANS )