It has been a little over a week since the two leaders of the world's nuclear club met behind closed doors in the Finnish capital of Helsinki.

Both U.S. President Donald Trump and Russian President Vladimir Putin, who own the lion's share of the world's nukes, said ahead of their first formal discussion that they would address the proliferation of nuclear weapons.

"If we can do something to substantially reduce them, I mean, ideally get rid of them, maybe that's a dream, but certainly it's a subject that I'll be bringing up with him," Trump said before the meeting. "The proliferation is a tremendous, I mean, to me, it's the biggest problem in the world, nuclear weapons, biggest problem in the world."

Similarly, the Russian leader said the two countries had a "responsibility for maintaining international security," citing their respective nuclear weapons arsenals.