Ri said on Monday the North's right to contermeasures included shooting down U.S. bombers "even when they are not inside the airspace border of our country".
Writing in the Atlantic website, former US Department of State official Joel S. Wit said: "A meeting with Foreign Minister Ri would be an important opportunity for the Trump administration to directly communicate its views to a North Korean official with ties to Kim Jong Un".
The measures follow an escalating war of words between North Korean leader Kim Jong Un and U.S. President Donald Trump.
But he said Trump's remarks are likely to harden North Korea's negotiating position if talks ever restarted.
Here's Bob woodruff. Reporter: American b-1 bombers and f-15 fighter jets took off in the night, flying farther north of the dmz than any time in almost two decades.
Trump later responded on Twitter, insulting Kim once more and appearing to threaten both men. North Korea has one nuclear test site - Punggye-ri.
The Pentagon said the mission in global airspace showed how seriously President Donald Trump takes North Korea's "reckless behavior".
Secretary of State Rex Tillerson says North Korea's Kim Jong Un is "being tested" by the strongest sanctions ever put in place by the USA and the worldwide community. "But last weekend, Trump ultimately declared war by saying again that our leadership will not last long".
Nikki Haley on North Korea: 'We're Not Going to Run Scared'
The North Korean foreign minister called Trump a "mentally deranged person, full of megalomania and complacence, the person chastised even by American people as 'Commander-In-Grief, ' 'Lyin King, ' and 'President Evil.'?"
He said sanctions would have no effect on Pyongyang's resolve to develop its nuclear weapons, with the ultimate goal being "balance of power with the U.S".
Mr Ri suggested to reporters on Friday in NY that the country could conduct an atmospheric hydrogen bomb test to fulfil Kim's vows.
North Korea has said it intends to build a missile capable of striking all parts of the United States with a nuclear bomb.
But on the fringes of the United Nations meeting this week, North Korean Foreign Minister Ri Yong-ho upped the tensions further, telling reporters Pyongyang might now consider detonating a hydrogen bomb outside its territory.
Tillerson won't say what the US response would be if Kim's government tested a hydrogen bomb in the Pacific Ocean.
"This mission is a demonstration of USA resolve and a clear message that the president has many military options".
The moves follow the adoption of a unanimous United Nations security council agreement on sanctions after North Korea conducted its sixth and most powerful nuclear test on 3 September.
Of that flight, Pentagon spokesperson Dana White said, "This is the farthest north of the Demilitarized Zone any USA fighter or bomber aircraft have flown off North Korea's coast in the 21st century".
North Korea in recent weeks detonated its sixth nuclear bomb and has test-fired intercontinental missiles - saying it needs to defend itself against hostility from the United States and its allies.