US President Donald Trump met one-on-one with Russian President Vladimir Putin behind closed doors today.

The long-awaited summit was overshadowed by the US president blaming his own country's past "foolishness and stupidity" for the two powers' hostile ties.

Here are some key comments from the joint press conference held after their meeting in Finland's capital Helsinki.

The Cold War a thing of the past - Putin

President Putin said today's negotiation with Mr Trump was frank, adding "I think we can call them a success".

He said the current tension in bilateral relations has no solid reason behind it.

"The Cold War is a thing of the past," he said.

Today both Russia and the US face a whole new set of challenges, he added.

Our relationship has changed - Trump

Mr Trump said: "If we are going to solve many of the problems facing our world, we will have to find ways to cooperate ... We have seen the consequences when diplomacy is left on the table."

"Our relationship has never been worse than it is now, however that changed as of about four hours ago. Refusing to engage will not accomplish anything."

He added: "I would rather take a political risk in pursuit of peace than risk peace in pursuit of politics."

The 'probe is a disaster for our country' - Trump

Mr Trump declared that the investigation into Moscow's alleged meddling in the US election had been a "disaster" for the US.

"I think that the probe is a disaster for our country. I think it's kept us apart. It's kept us separated. There was no collusion at all. Everybody knows it."

Mr Trump added: "It was a clean campaign. I beat Hillary Clinton easily."

Putin 'powerful in his denial' - Trump 

Mr Trump noted the Russian president's "powerful" denial of any interference in the 2016 US election.

"I have great confidence in my intelligence people but I will tell you that President Putin was extremely strong and powerful in his denial today," Mr Trump said. 

'We should be guided by facts' - Putin

Mr Putin said allegations of meddling in the US election are complete nonsense. 

Could you name a single fact that would definitely prove the collusion, he asked.