This applied even when they were not in North Korean airspace, the minister added.
This is not the first time that North Korea has used the phrase "a declaration of war" in relation to the United States.
But Mr Ri's comments are a response to the US president's tweet that Mr Ri and North Korean leader Kim Jong-un would not "be around much longer" if they continued their rhetoric.
The world "should clearly remember" it was the US that first declared war, Mr Ri said, in a rare statement to Western media as he left New York.
The foreign minister had addressed the UN General Assembly on Saturday.
In a fiery speech he described Mr Trump as a "mentally deranged person full of megalomania" on a "suicide mission".
The two sides have been engaged in an increasingly angry war of words. Despite weeks of tension, experts have played down the risk of direct conflict between the two.
"In light of the declaration of war by Trump, all options will be on the operations table of the supreme leadership of the DPRK [North Korea]," Mr Ri added on Monday.
North Korea has continued to carry out nuclear and ballistic missile tests in recent weeks, in defiance of successive rounds of UN sanctions.
The country's leaders say nuclear capabilities are its only deterrent against an outside world seeking to destroy it.
After the North's latest and most powerful nuclear test earlier this month, the UN Security Council approved new sanctions on the country.
The rhetoric on both sides may have got out of hand already but the real question is what practical consequences might ensue from the war of words between Washington and Pyongyang?
It should be remembered that the Korean peninsula is not at peace - the Korean conflict of the 1950s was only brought to a halt by an armistice, not a peace treaty.
But it is actions that are likely to provoke renewed fighting, not just words.
The latest North Korean threat to shoot down US warplanes comes in the wake of a recent US patrol that took its B1-B Lancer bombers and their accompanying F-15 fighter escorts over waters to the east of North Korea - the furthest north US warplanes have flown for several months, albeit still outside Pyongyang's airspace.
The US believes it has every right to do this. But if one day Pyongyang judges that these aircraft are on an offensive mission - what then?
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