Should they be approved, the measures would be the toughest sanctions ever passed against Pyongyang.
A South Korean presidential office spokesman said on Tuesday: "North Korea needs to realise that a reckless challenge against worldwide peace will only bring about even stronger sanctions against them".
North Korea described the test, on September 3, as the detonation of a hydrogen bomb that could be delivered on a missile.
USA diplomats have called for an oil embargo, an assets freeze against leader Kim Jong-Un, a ban on textiles and an end to payments of North Korean guest workers in response to the nation's sixth nuclear test last week.
Whatever final text was adopted, she hoped it would "have significant consequences in terms of greater economic pressure on North Korea".
Katia makes landfall on Mexico's Gulf coast, weakens to tropical storm
It was expected to gain some strength but the effects of Irma were seen eventually weakening that storm. Many parts of Florida are in Irma's projected path and could be hit by the storm as early as Saturday.
One of the main guidelines of this proposal identified nine cargo ships that broke previous United Nations sanctions by conducting commercial activities on behalf of North Korea.
China has held the position that stronger sanctions would not be helpful in halting North Korea's nuclear programme.
John McCain says the USA needs to step up actions against North Korea and send a message to leader Kim Jong Un that aggressive acts will lead to his country's destruction.
"We have frozen their accounts, which means they can not withdraw (money)", a staff member at a Yanji branch of China Construction Bank told AFP.
"The world will witness how the DPRK tames the USA gangsters by taking a series of actions tougher than they have ever envisaged", the statement said, referring to the country's formal name, the Democratic People's Republic of Korea.
There are a few things that made it through the negotiating process - for instance, a ban on textile exports from North Korea, for instance.
Textiles were North Korea's second-biggest export after coal and other minerals in 2016, totaling $752 million, according to data from the Korea Trade-Investment Promotion Agency.
"A full assessment (of the data) makes it possible to conclude that the North Korean nuclear test has not caused any environmental impact in China", the Chinese Ministry of Environment said in a brief statement on its official microblogging account.