The move is said to be unlike previous US efforts, in which the USA has spent weeks, and sometimes months, carefully crafting language with China before presenting the resolution to the rest of the Security Council for a vote.
The new actions would coincide with an intensifying effort to punish North Korea.
While public antipathy towards Koreans does not appear to have escalated in reaction to the North's latest nuclear test and missile launches, the community has been the target of abuse by Japanese nationalists after similar incidents in the past.
North Korean ally China and neighboring Russian Federation have resisted further sanctions, although both nations' UN representatives participated in discussions about a new round of sanctions this week.More news: North Korea urges nuclear buildup on its anniversary
"A special measure is urgently needed to stop their recklessness".
The basketball great has been to North Korea several times following his first visit in 2013. But Xi agreed that they "will not be putting up with what's happening in North Korea", the U.S. president said. "The question is what happens with an extraordinarily hardline resolution and U.S. pressure to do something quickly".
"Now is not the time to talk to North Korea", Trump was quoted as saying in a White House readout highlighting his Tuesday discussion with May. "We have been communicating with the DTI secretary and I think it was yesterday and the other day, we have gotten direction from the (presidential) palace to support the U.N. Security Council".
U.S. Ambassador Nikki Haley said at an emergency council meeting earlier this week after North Korea's sixth and largest nuclear test that the Trump administration wants to put the resolution to a vote Monday.
However it remained unclear whether Beijing, the North's key ally, would be willing to back, or enforce, new sanctions at the UN Security Council, where it is a veto-wielding permanent member.
A US proposal for new United Nations sanctions against North Korea would target the country's leader Kim Jong Un and key members of his regime with a full asset freeze and world-wide travel ban and clamp an embargo on oil and textile trade, according to a draft of the proposal. Trump refused to comment however, when asked about details, on how the USA would negotiate with North Korea, saying he would not be broadcasting his intentions. He explained that only a united council can provide the pressure needed to enable successful negotiations to take place to denuclearize the Korean Peninsula.
"Without political and diplomatic tools, it is impossible to make headway in the current situation; to be more precise, it is impossible", said Putin at a news conference with Moon.