Washington has invited the Russian leader to visit in 2019, but such a visit could prove controversial because USA intelligence agencies have concluded that Moscow meddled in the 2016 United States presidential election in favour of Mr Trump.
"These are serious questions, and it's a real shame that there's a tendency to underestimate them", Putin continued, according to Reuters.
He said that if the USA puts intermediate-range missiles in Europe, Russia will be forced to take countermeasures.
Any such inspections - if they were to happen - should not be unilateral but should take place in both countries, he added.
"The proper definition of denuclearization of the Korean Peninsula is completely eliminating the American nuclear threat to North Korea before eliminating our nuclear capability", the statement reads, according to CNN.
He noted that the US also appears to show little interest in extending the New START nuclear arms reduction treaty, which expires in 2021.
Amid a litany of complaints over Washington's policies, Putin had one nice thing to say about the United States: He welcomed Trump's decision to withdraw the US military from Syria. - Ok, we'll survive and will ensure our own security which we know how to do. "Some analysts are already expressing such ideas that maybe, perhaps, it's not such a bad thing, and we might be able to use it, but lowering the threshold might lead to a global nuclear catastrophe and secondly the use of ballistic missiles, not nuclear ballistic missiles".
Putin said that the US announcement it will withdraw its troops from Syria is "the right thing to do" though he expressed skepticism about whether it will actually take place. Meanwhile, if something like it occurs, God forbid, it can lead to the death of the whole civilization and, maybe, our planet.
Russia's hopes for repairing ties with the US under President Donald Trump have fizzled amid allegations of Russian meddling in the 2016 election - charges Putin has denied.
British Prime Minister Theresa May faces no-confidence vote
She would be toppled if 158 of her party's 315 lawmakers don't support her in a ballot set to take place after 1 p.m. Former Environment Secretary Owen Paterson accused May of acting like a "supplicant" in dealings with the EU.
"We have an agreement from 2003", he said, becoming perhaps the first Russian official since the incident to mention the formal agreement between Russia and Ukraine declaring the Kerch Strait and Sea of Azov as shared territorial waters.
"We are essentially witnessing the breakdown of the global arms control order and (the start of) an arms race", he said.
The deal bans ground-launched medium-range missiles, with a range of 500-5,500km (310-3,400 miles).
Mr Putin also addressed his country's strained ties with the United States, saying he did not know if he would meet President Donald Trump soon or not.
"We will have to ensure our security", Putin said during the news conference that lasted almost four hours.
Putin, who was addressing more than 1,000 reporters from around the world, many of them holding up signs to attract his attention, faced a tougher task defending his domestic record.
Putin showed no sign of backing down from Russia's stance on Ukraine, and accused his Ukrainian counterpart of provoking a naval stand-off with Russian Federation to boost his electoral prospects.
The Russian president noted that the nation's hard currency reserves have increased from $432 billion at the start of the year to $464 billion now.
Putin noted that it would be proper for the U.S.to leave Syria since it is there illegally, without invitation from the Syrian government in Damascus - as Russian Federation was - nor authorization from the United Nations Security Council.
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