Ri is set to speak at the United Nations on Friday, 22 September.
The secretary of state also hinted that the current pressure campaign against North Korea is starting to bear fruit.
"It's important to go after illicit networks", David Maxwell, an expert on North Korea and security at Georgetown University, told BuzzFeed News.
Mr Trump told the UN "Rocket Man is on a suicide mission for himself and his regime" and added that if the USA was "forced to defend itself or its allies, we will have no choice but to totally destroy North Korea".
Asked by reporters what he thought of Trump calling North Korean leader Kim Jong-un "rocket man", Ri added: "I feel sorry for his aides".
Earlier, national security advisor H.R. McMaster said Trump would take more action to stop North Korea "short of war".
On Thursday, South Korea's Moon said sanctions were needed to bring Pyongyang to the negotiating table and force it to give up its nuclear weapons, but Seoul was not seeking North Korea's collapse.
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Ri is slated to make a United Nations speech on Friday. Among the issues facing the assembly this year are North Korea's nuclear developement, violence against the Rohingya Muslim minority in Myanmar and the debate over climate change.
"Diplomacy is the preferred option, when I say that, that means we still have a lot of tools in our tool kit that we can deal with North Korea".
North Korea funds its evil nuclear programme via dealings with foreign companies and individuals and the United States of America today announced it was cracking down on such arrangements.
"The key to it, we think, is to work together with all our friends and partners here in the United Nations, get the Chinese to put more economic pressure on Pyongyang".
One method employed by the State Department limits the number of North Korean guest workers in other countries.
Over the summer, Treasury took actions against the Bank of Dandong over concerns that it was participating in illicit financial activities with North Korea - an early signal to Chinese financial institutions of US willingness to increase pressure on entities that do business with Pyongyang. China, which has condemned the North's nuclear ambitions, is the nation's closest ally.
Nauert pointed out that North Korea is not just a concern for the United States.
President Donald Trump on Thursday signed an executive order expanding his authority to target people and institutions that do business with North Korea.
So far, North Korea has been all bark and no bite.
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