US officials told the Reuters news agency that Washington had been speaking to partners in the Asia-Pacific region, such as Japan, South Korean and Singapore, over how to crack down on ships suspected of violating sanctions on the North.
The plan could see US Coast Guard ships deployed in the region to stop and search vessels.
Trump threatens phase two
South Korea welcomed the new round of sanctions.
"New US sanctions will alert those who are illegally trading with North Korea and therefore bolster the international community to carry out resolutions from the UN Security Council," the South Korean Foreign Ministry said.
US President Donald Trump, who said the measures were "the heaviest sanctions ever imposed on a country," appeared to threaten military action against North Korea if the sanctions failed.
"If the sanctions don't work, we'll have to go phase two," Trump said. Without elaborating further, he added: "Phase two may be a very rough thing, may be very, very unfortunate for the world."
Depriving the North
The sanctions are Washington's latest attempt to cut off "illicit avenues used by North Korea to evade sanctions," US Treasury Secretary Steven Mnuchin said.
Trump said she would use her presence at the end of the Olympics to emphasize the US commitment to a "maximum pressure campaign to ensure that the Korean Peninsula is denuclearized."
In a possible attempt to reassure Washington, Moon said that South Korea was the "last" country that would be willing to acknowledge North Korea as a nuclear state. He added that any talks about improving relations between the two countries must also include talks on nuclear disarmament.
"North Korea's participation in the Winter Olympic Games has served as an opportunity for us to engage in active discussions between the two Koreas and this has led to lowering of tensions on the peninsula and an improvement in inter-Korean relations," Moon said.
South Korea's Presidential Blue House said that there were no official opportunities for the US and North Korean officials to meet, suggesting that a run-in between Pyongyang's delegation and Ivanka Trump was unlikely.