Donald Trump says a productive dialogue between America and Russia is good for both countries and "is good for the world".
Mr Trump added he had discussed disagreements between the countries "at length" with Russian leader Vladimir Putin during a day of meetings and accepted that relations between them have never been worse.
However, Mr Trump added that he thinks "that changed as of about four hours ago".
Mr Trump said at the start of the summit that he thinks he can have an "extraordinary relationship" with the Russian leader.
The American president said their two countries have "great opportunities", given that they have not been getting along over the past few years.
Talking of his relationship with Mr Putin, he said he thinks that "the world wants to see us get along".
Their discussions included the military, missiles, nuclear weapons and China.
President Trump speaks at a press conference in Helsinki (Pictures: White House).
During a press conference alongside Mr Putin in Helsinki, Mr Trump said: "Today's meeting is only the beginning of a longer process but we've taken the first steps towards a brighter future and one with a strong dialogue and a lot of thought.
"Our expectations are grounded in realism but our hopes are grounded in America's desire for friendship, cooperation and peace."
Earlier, the American president blamed the United States for the current low point in US-Russia relations:
The summit was condemned in advance by members of Congress from both parties after the US indictment last week of 12 Russian military intelligence officers accused of hacking Democrats in the 2016 election to help Trump's presidential campaign.
Mr Trump, who had sought to lower expectations about what will be achieved, told reporters during a breakfast with Finland's president Sauli Niinisto that he thought the summit would go "fine".
Ahead of his meeting, the US President also tweeted about how he has been "thanked" by leaders from NATO nations, following a summit in Brussels last week:
Last week, Mr Trump visited the UK when he described the relationship between the UK and the US Armed Forces as "vital".