The draft resolution circulated to the Security Council members comes after Pyongyang’s sixth nuclear test and repeated missile launches.
North Korea also claims to have developed a hydrogen bomb and continues to threaten to strike the US.
China and Russia are both expected to oppose further sanctions.
Pyongyangis already under highly restrictive sanctions imposed by the UN that are intended to force the leadership to curtail its weapons programs.
In August, a new round of sanctions banned exports including coal, costing North Korea an estimated $1 billion – about a third of its entire export economy.
However, some trade avenues remain open to it.
The draft US proposal calls for a total ban on supplying a range of oil products to North Korea and a ban on its textile export industry.
It also suggests freezing the assets of Kim Jong-un and the North Korean government, as well as banning him and other senior officials from travelling.
North Korean laborers would also be banned from working abroad, principally in Russia’s Far East and China.
Remittances from foreign earnings and textile exports are two of the most important remaining sources of income for North Korea.
However, it is not clear how China and Russia, which both supply oil to North Korea and wield vetoes at the Security Council, will respond to the US move.
On September 7, China’s foreign minister Wang Yi told reporters that the council should respond further “by taking necessary measures”, but did not elaborate.
Wang Yi added that “sanctions and pressure are only half of the key to resolving the issue. The other half is dialogue and negotiation.”
China is both North Korea’s and the US’s biggest trade partner, and has supported recent sanctions against it.
President Vladimir Putin has argued that the amount of oil Russia exports to North Korea – some 40,000 tonnes – is negligible.
“It is not worth giving in to emotions and driving North Korea into a corner,” President Putin said.
Both China and Russia have been pushing for an alternative solution.
They are proposing that the US and ally South Korea stop their military drills – which anger the North – and end the deployment of the controversial anti-missile THAAD system in South Korea, in return for North Korea ceasing its nuclear and missile program.
The proposal has been rejected by the US and South Korea.
On September 7, South Korea’s military announced it had completed the deployment of THAAD, Yonhap reported.
South Korean President Moon Jae-in also met with Japan’s PM Shinzo Abe, where both agreed to push for greater sanctions. Shinzo Abe called for “the greatest possible pressure” to be put on North Korea.
President Donald Trump had previously warned the US could cut off trade with countries that do business with North Korea.
The US has indicated that if the resolution is not passed when the Security Council meets on September 11 it may impose its own sanctions unilaterally.
Treasury Secretary Steve Mnuchin told reporters on September 6: “We believe that we need to economically cut off North Korea.
“I have an executive order prepared. It’s ready to go to the president. It will authorize me to… put sanctions on anybody that does trade with North Korea.”
President Donald Trump and Chinese President Xi Jinping also discussed North Korea over the phone on Wednesday, where they agreed to “take further action”, said a White House statement.
Donald Trump, who has previously threatened a military response to North Korea, told reporters this was “not our first choice”, but did not rule it out.
He added: “President Xi would like to do something. We’ll see whether or not he can do it. But we will not be putting up with what’s happening in North Korea.”
Chinese state news agency Xinhua reported that President Xi called for a “peaceful settlement of the issue” involving “dialogue combined with a set of comprehensive measures”.
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