The statement, which was tabled by the US, would also tell North Korea not to conduct further nuclear tests.
It has conducted five so far, and last week analysts warned that the country's nuclear test site was "primed and ready" for a sixth.
Instead, North Korea tested a missile Sunday, which was said to have failed
, provoking more calls for the country to cease its hostile acts.
UN diplomats said the proposed statement of condemnation had consensus from the other 14 Council members, including China, North Korea's biggest ally and a Council permanent member.
Russia has a long record of vetoing resolutions pushed by the US. Last week, it used its veto power
to block an attempt to condemn the killing of dozens of people in a suspected Syrian chemical attack. In that instance, China abstained.
Little hope is held for reviving the motion against North Korea -- one diplomat said it was unlikely the Security Council would be able to resolve differences on the statement.
Next week, US Secretary of State Rex Tillerson will chair a minister-level meeting on the North Korean issue at the UN.
Haley: Ball's in N. Korea's court
US Ambassador Nikki Haley told UN reporters it was "up to North Korea to avoid further trouble."
She said that she wanted Pyongyang to see that the US was not an aggressor.
"I think it's important that North Korea knows we're not trying to pick a fight, so don't try and give us one," she said.
"And, it's up to them to kind of see it. We've said it as clearly as we can possibly say it. You know, the ball is in their court. They shouldn't try and play at this point."
The reclusive nation, which has long pursued nuclear ambitions, conducted its fifth nuclear test last September, its most powerful so far. It is not a signatory to the Comprehensive Test Ban Treaty, the global ban on nuclear explosive testing.