US President Barack Obama and Cuban leader Raul Castro shook hands before the summit began
He was speaking just before the seventh Summit of the Americas in Panama City.
Mr Obama and Cuban leader Raul Castro shook hands as the opening ceremony began, their first encounter since a December detente.
But their historic formal talks due on Saturday could be overshadowed by tensions between Venezuela and the US.
Mr Obama told a forum of civil society leaders in Panama City that ?the days in which our agenda in this hemisphere presumed that the United States could meddle with impunity, those days are past?.
At past Summits of the Americas, which bring together the leaders of North, Central and South America, the US has come in for criticism for its embargo against Cuba and its objection to having Cuba participate in the gatherings.
This seventh summit is the first which Cuba will attend and much of the attention will be focussed on the body language between the former foes.
Barack Obama and Raul Castro are due to meet again later on Saturday. It will be the first formal encounter between the leaders of the US and Communist-run Cuba in more than five decades.
Before the summit began, the US president stressed that he hoped the thaw in relations would improve the lives of the Cuban people.
?Not because it?s imposed by us, the United States, but through the talent and ingenuity and aspiration and the conversation among Cubans, among all walks of life. So they can decide what is the best course of prosperity.?
Later, Mr Obama and Mr Castro joined representatives from 35 nations for the summit?s inauguration ceremony.
A marching band and children in national dress of the participating countries waved flags as the summit opened to applause.
Mr Obama?s speech before the summit came a day after the State Department recommended that Cuba be removed from the US lists of countries which sponsor terrorism.
Its presence on the list has been one of the main hurdles on the way to closer ties between the two countries.
The president said on Thursday that all he was waiting for now was a recommendation from his advisers, leaving many expecting an announcement at the summit.
The smooth progress made between Cuba and the US stands in contrast to the bumpy ride that have been relations between Venezuela and the US over the past months.
The two countries have not exchanged ambassadors for more than six years, but tensions rose last month when the US imposed sanctions on a group of Venezuelan officials it accuses of human rights abuses.
As part of the sanctions, Mr Obama issued an executive order declaring Venezuela a threat to the national security of the United States.
President Maduro has collected more than 10 million signatures demanding its repeal.
Their meeting at the summit, while less historic than the one between Mr Castro and Mr Obama, is drawing as much attention for its unpredictability.
Mr Maduro sent out mixed messages on Friday.
In a clear swipe at the US, he visited a monument to the victims of the 1989 US invasion of Panama just hours after he landed.
But he also said that it was ?time not for imperialism, but for peace?.
?We?re in a battle of ideas, in a fight so that Venezuela is respected, we?re coming here in a constructive spirit, to make history through respect,? he said.