The resolution, aimed at imposing tougher sanctions on North Korea, is backed by China.
The measures would for the first time require UN member states to inspect all cargo to or from North Korea.
US Ambassador to the UN Samantha Power said it would be the strongest set of sanctions imposed by the Security Council in more than 20 years.
A vote is expected at the weekend.
North Korea’s launch of a long-range rocket in February and a nuclear test in January were widely condemned as a flagrant violation of UN resolutions.
China also condemned North Korea’s actions but it has previously been reluctant to endorse sanctions that could threaten its neighbor’s stability.
“For the first time in history, all cargo going in and out of the DPRK (North Korea) would be subjected to mandatory inspection,” Samantha Power said after presenting the draft resolution measure to the Security Council.
“These sanctions, if adopted, would send an unambiguous and unyielding message to the DPRK regime. The world will not accept your proliferation. There will be consequences for your actions.”
February 25 announcement followed weeks of negotiations between the US and China that culminated in talks in Washington this week between Secretary of State John Kerry and Chinese Foreign Minister Wang Yi.
North Korea insists its missile program is purely scientific in nature, but the US, South Korea and even its ally China say such rocket launches are aimed at developing inter-continental ballistic missiles.
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