Russian Ambassador Vassily Nebenzia told reporters that a vote on Monday would be "a little premature. I don't think we will be able to rush it so fast."
Russia argues that sanctions alone will not resolve the North Korea crisis and are backing a Chinese proposal for talks based on a freeze of North Korea's nuclear and missile tests in exchange for a suspension of US-South Korean military drills.
Nebenzia said a new resolution should stress the need for diplomatic steps.
"We want a reference to the need for a political dialogue based on the recent initiatives that have been undertaken," Nebenzia said.
Haley on Monday rejected the Russian-Chinese proposal as "insulting."
"When a rogue regime has a nuclear weapon and an ICBM pointed at you, you do not take steps to lower your guard. No one would do that. We certainly won't," she said.
The United States has yet to circulate the draft, but diplomats said it will likely propose cutting oil supplies to North Korea, banning tourism and sending back North Korean laborers working abroad.
French Ambassador Francois Delattre said that he expected negotiations on the new measures to move quickly, and suggested that Russia and China could be brought on board.
During an emergency council meeting on Monday, "nobody ... opposed new sanctions so we believe there is clearly some space, some political space to move forward and to move forward fast," Delattre said.
The Security Council last month unanimously decided to impose new sanctions on North Korea after it tested two intercontinental ballistic missiles (ICBM) that some experts say brought the US mainland within range.
Those included a total ban on North Korea's exports of coal, iron and seafood, and a freeze on work permits for North Korea foreign workers whose earnings are a source of hard currency for the regime.
UN human rights investigators estimate that more than 50,000 North Koreans have been sent abroad, mostly to Russia and China, generating between $1.2 billion and $2.3 billion per year.