Council diplomats, speaking anonymously because discussions were private, said the USA, which is in charge of drafting council statements and resolutions on North Korea, had dropped the call for "dialogue" as part of its effort to toughen the text.
Last month, the council was united in strongly condemning the launch of three missiles and expressed serious concern over Pyongyang's "increasingly destabilizing behavior".
Russian Federation had blocked an earlier version of the statement - which comes after North Korea carried out a failed test on Sunday - even though China, Pyongyang's ally, had expressed its support for it.
In recent months North Korea has refused to buckle to worldwide pressure and continued to develop both its nuclear and test missiles.
South Korea's acting president, Hwang Kyo-ahn, at a meeting with top officials on Thursday, repeatedly called for the military and security ministries to maintain vigilance.
"We are conducting a practical and more intensive exercise than ever", South Korean pilot Lieutenant Colonel Lee Bum-chul told reporters.
With Donald Trump in power since January, North Korea has returned to its tactic of missile provocations, while Washington has urged for China's help to bring Pyongyang back to the negotiating table, although it has not ruled out the possibility of military action.
Previous statements denouncing missile launches "welcomed efforts by council members, as well as other states, to facilitate a peaceful and comprehensive solution through dialogue". "I think at the end of the day we realized North Korea is a problem and no one on the council wants to see North Korea move forward with any sort of testing or strikes ... and if we have to start looking at sanctions or other actions we will". However, this time the statement reportedly dropped "through dialogue" from the draft, which Russian Federation had insisted it be included, according to Reuters.
There has been some confusion over the whereabouts of a USA aircraft carrier group after Trump said last week he had sent an "armada" as a warning to North Korea, even as the ships were still far from Korean waters.
"We are evaluating all of those options", he said.