"We have discussions on everything from trade to military to missiles to nuclear to China", he added, while seated beside his Russian counterpart.
Putin, for his part, said he and Trump have maintained regular contact, including talking by phone and meeting at global events. "It is great to be with you", Trump told Putin, before shaking hands briefly and heading into talks, which are being closely watched around the world.
The summit, which was being closely monitored by rattled world capitals, was condemned in advance by members of Congress from both parties after the USA indictment last week of 12 Russian military intelligence officers accused of hacking Democrats in the 2016 election to help Trump's presidential campaign.
In an interview on Sunday, Trump downplayed the significance of the tete a tete.
"I think we will end up having an extraordinary relationship". Frankly, we have not been getting along very well for the last number of years. "Whoever says we are foes is spreading fake news".
With that in mind, a senior House of Representatives Republican told CBS's "Face the Nation" that Trump should ask Putin in Helsinki which airport the Russian hackers will be extradited to for being taken into US custody.
Trump also said that "getting along with Russian Federation is a good thing, not a bad thing".
That's something many Americans have wondered, since Trump's recent North Atlantic Treaty Organisation meeting has been called a disaster by critics.
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Shortly before the summit opened, Trump was asked if he would press Putin over alleged Russian meddling in the United States presidential campaign.
"He didn't mention [the Russian] election meddling in the United States, cybercrime during the 2016 election and the indictment of 12 Russians in the last few days by the special council", he said.
Friday's charges against the 12 Russian officers alleging they hacked Democratic computer networks in 2016 represented the most detailed US accusation yet that Moscow meddled in the election to help Trump.
The encounter comes three days after special counsel Robert Mueller indicted 12 Russian intelligence officers, accusing them of meddling in election to help Trump win the White House.
Trump adds that relations between the USA and Russian Federation have never been worse.
Foreign policy experts have raised concerns that during one-on-one talks without a clear agenda, Trump might seek to make a grand gesture that offers Putin serious concessions on Crimea, Syria or Ukraine.
Political opponents have urged Trump, who denies collusion, to use the summit to challenge Putin about the hacking and other malign activities.