"I greeted Bush with this hand eight years ago; I want to be your friend," Chavez told Obama, according to a Venezuelan presidential press office statement.
Obama's speech follows a flurry of gestures from Washington, such as dropping restrictions on Cuban-Americans visiting relatives in Cuba and permitting US companies to bid for telecommunications licences.
Havana has also suggested that the two nations could be prepared to end years of hostilities.
Raul Castro, the Cuban president, has said his country is open to talks with Obama on "everything", including human rights, press freedom and political prisoners.
Obama noted the offer but added that any negotiations had to be substantial.
"I am not interested in talking for the sake of talking,'' he said.
"But I do believe that we can move US-Cuban relations in a new direction.''
The US president also said that he sought an "equal partnership" with Latin American states during his administration.
Marwan Bishara, Al Jazeera's senior political analyst, said Obama recognised that the US had interfered in the southern hemisphere in the past but also said that the US could not be blamed for the world's ills.
The weekend-long summit is nominally to discuss regional security and the global financial crisis.
|Obama's visit was welcomed by
many in Trinidad and Tobago [Reuters]
However, many of the 34 leaders attending the summit see Cuba as a priority and argue that efforts by the US to marginalise the state are obsolete and have instead only isolated the US government in the region.
In a joint statement issued last December, Latin American countries, including Argentina, Brazil and Mexico, called for the US to scrap its embargo against Cuba.
On Thursday, Evo Morales, the Bolivian president, repeated the call and urged the Bolivarian Alternative for the Peoples of our America (ALBA) summit to present a joint resolution at the summit of the Americas for an end to the US embargo.
He said that Obama had a "moral and ethical obligation" to comply.
Chavez has condemned Cuba's exclusion from regional groups and says he will not endorse the draft declaration from the Port of Spain summit.
The fifth summit of the Americas is the first to be held in the Caribbean.
The last gathering, in Mar del Plata, Argentina, was met with large demonstrations against the US and then-president George Bush, Obama's predecessor.