Ri reportedly added that "We have no idea about what actions could be taken as it will be ordered by leader Kim Jong Un."
Ri is in New York attending the United Nations General Assembly.
Such a test would be considered a major provocation by Washington and its allies.
Ri's threat is significant because such a detonation would move North Korea's nuclear weapons activities beyond its borders for the first time.
The communist dictatorship's previous nuclear tests have taken place in its isolated mountains.
Hydrogen bombs are more powerful by an order of magnitude than the atomic bombs that North Korea tested in previous years. The country claims that an atomic test it carried out early this month was an H-bomb.
The apparent threat comes after Kim issued a rare statement calling US President Donald Trump "deranged" and warning he "pay dearly" for his threats.
In his maiden speech to the UN two days ago, Trump said he would "totally destroy" North Korea if it attacked the US or one of its allies.
"Far from making remarks of any persuasive power that can be viewed to be helpful to defusing tension, he made unprecedented rude nonsense," Kim said today.
"A frightened dog barks louder," Kim said. "He is unfit to hold the prerogative of supreme command of a country, and he is surely a rogue and a gangster fond of playing with fire."
Pyongyang launched an intercontinental ballistic missile over Japan exactly one week ago, earning a fresh new round of sanctions.
Seoul's spy agency also warned the North could launch an ICBM on a standard trajectory toward the Pacific Ocean around its founding anniversary of the ruling Workers' Party of Korea on October 10.
Australian nuclear disarmament campaigner John Hallam warned Trump's remark at the UN General Assembly would make North Korea feel more backed into a corner.
He wanted the comments were likely to cause conflict rather than bringing about a potential solution and that it could become nuclear very quickly.
"It's unlikely, though just possible, that the DPRK will in fact back down, and much more probable that he will do as he has done up to this point: Do precisely that which his interlocutor has forbidden him to do," he said.
"The US having established a red line, the DPRK has always immediately crossed it."
- additional reporting news.com.au
