CHEQUERS, England (REUTERS) - US President Donald Trump said he would discuss substantial reductions to nuclear weapons when he meets Russian President Vladimir Putin but cautioned that a "rigged witch hunt" in the United States was hampering efforts to improve relations.

Trump and Putin, who control the world's two biggest nuclear arsenals, are due to meet on Monday in Helsinki, a venue which evokes memories of Cold War show-downs between the Soviet Union and the United States.

"The proliferation is a tremendous, I mean to me, it's the biggest problem in the world, nuclear weapons, biggest problem in the world," Trump said alongside British Prime Minister Theresa May at her Chequers country residence.

"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 of his upcoming meeting with Putin.

Trump added the nuclear arsenals were "also a very expensive thing but that's the least important."

Though Trump has not so far given specific details about what nuclear arms control treaties they would like to talk about, he and Putin are likely to discuss the possibility of extending the "New Start" treaty - a pillar of arms control.

They are also likely to discuss what to do about another pact known as the Intermediate-Range Nuclear Forces Treaty (INF) to try to dampen a high-risk nuclear rivalry between the two former Cold War foes.

But Trump cautioned that it was hard to do substantive deals with Russia because of an investigation into suspected Russian interference in the 2016 US election, a probe Trump cast as"rigged witch hunt".

"We have this stupidity going on, pure stupidity, but it makes it very hard to do something with Russia because, anything you do, it's like: 'Russia, oh he loves Russia'," Trump said.

"I love the United States but I love getting along with Russia and China and other countries."

"I call it the rigged witch hunt. I think that really hurts our country and it really hurts our relationship with Russia," said Trump who denies any collusion with Russian meddling in the election.

Trump was speaking shortly before the Justice Department in Washington announced that a federal grand jury had indicted 12 Russian military intelligence officers on charges of hacking the computer networks of 2016 Democratic presidential candidate Hillary Clinton and the Democratic Party.

Trump added that he would raise alleged Russian election meddling with Putin.

When asked if there was any way for relations with the Kremlin to improve while Russia continues to occupy Crimea, which it annexed 2014, Trump said: "Yes, I think so."

Trump said Putin would not have dared to annex Crimea if he had been in the White House.

"This was an Obama disaster and I think if I had been president then, he would not have taken over Crimea."

"We haven't taken off the sanctions, the sanctions are biting," Trump said.

"I have taken over a lot of bad hands and I'm fixing them one by one and I know how to fix them."