Washington has led the international drive to punish the rogue state after it detonated a nuclear device this month.
The US had originally pushed for a strict oil embargo, as well as a freeze on the assets of North Korean leader Kim Jong-Un.
But late Sunday, diplomats said the asset freeze had been dropped from the draft, and it now foresaw a progressive tightening of the oil taps, instead of something sudden and complete.
Of five key original measures, a ban on textile exports from North Korea remained.
Britain and France -- permanent Security Council members along with the US, China and Russia -- have given Washington their unequivocal backing.
Francois Delattre, the French ambassador to the UN, told AFP: "Maximum pressure today in the form of sanctions is our best hope for promoting a political settlement tomorrow and the best antidote to risks of confrontation."
The sticking point will be opposition from Russia and China, the North's two main backers, who are wary of anything that might force the collapse of the regime and the resulting exodus of refugees.
In addition to bending somewhat to Moscow and Beijing, Washington has dangled the prospect of military action or cutting economic ties with countries that continue to have trade links with the North. Some 90 percent of North Korea's exports are destined for China.
"It is only possible to criticise and rebuke China and Russia for not enforcing the sanctions if they vote for it at the UN Security Council," he said.
"That's why I think the US tried to draw a UN sanctions resolution that China and Russia will participate in even if it is not fully satisfactory, which has led to the easing of the initially very strong draft proposal.
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