U.S. Ambassador Nikki Haley circulated the missive in her role as president of the Security Council for the month of April.
Russian Federation wanted to include language contained in a previous resolution stressing the need to achieve a solution through dialogue, council diplomats said. "They shouldn't try to play it at this point".
United Nations diplomats said the proposed statement had consensus from the other 14 Council members, including China, North Korea's biggest ally and a Council permanent member.
The council also warned the North of "further significant measures, including sanctions".
Tensions have escalated over North Korean moves to accelerate its arms programs, including developing an intercontinental ballistic missile that could reach the United States.More news: Cannot be complacent about potential threat of N. Korean missiles - UK minister
The Trump administration is focusing its North Korea strategy on tougher sanctions, possibly including an oil embargo, a global ban on its airline, intercepting cargo ships and punishing Chinese banks doing business with Pyongyang, Reuters reported last week, citing USA officials.
In a unanimous statement, the council demanded that North Korea "conduct no further nuclear tests", saying Pyongyang's "illegal missile activities" were "greatly increasing tension in the region and beyond".
The failed test last Saturday came amid a period of high tension, as United States apparently tried to pressure Pyongyang to forego its nuclear and missile programs under threat of military intervention.
"Russian Federation blocked it", Rycroft said, expressing surprise at Russia's position and noting that Pyongyang ally China had been on board with the version pushed by the USA on Wednesday.
Whether agreement can be reached on a statement remains to be seen.More news: Police, protesters clash ahead of Le Pen rally
Ahead of the "Day of the Sun" on April 15, one of the biggest celebrations in the North Korean calendar, North Korea analysts said satellite images showed Pyongyang was "primed and ready" for a sixth nuclear test.
Next week, US Secretary of State Rex Tillerson will chair a minister-level meeting on the North Korean issue at the UN. We've said it as clearly as we can possibly say it.
It says the meeting will give council members an opportunity to discuss ways to maximize the impact of existing United Nations sanctions "and show their resolve to respond to further provocations with significant new measures".
It was the fifth time this year that the council has adopted a press statement on North Korea.More news: Ontario to tax foreign buyers, expand rent control to cool housing market
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