"We have a very strong friendship between the two countries, but we can always make it stronger," Obama told Lula.
"[The US] has a unique and exceptional position to improve relationships with Latin America"
Luiz Inacio Lula da Silva, Brazilian President
During the meeting at the Oval Office, Obama praised Brazil as a "progressive" and "forward-looking" leader in the world.
Lula discussed US policy towards Brazil's neighbours in Latin America and urged Obama to improve relations with Cuba and Venezuela.
Lula, as the first Latin American leader visiting the White House, told Obama that the new US government has a "unique and exceptional position to improve relationships with Latin America."
He also expressed wishes to co-operate with the US to revive the World Trade Organisation's (WTO) Doha round of global trade talks.
Thomas Shannon, the US assistant secretary of state for western hemisphere affairs, said earlier this week that Lula's visit was a sign of increasingly close ties between Brazil and the US.
"This, from our point of view, is a great opportunity for the United States to build on an important relationship that we have with Brazil," he said, noting an established relationship between the two countries on alternative energy sources.
The two countries would also expand their co-operation on climate change and environmental protection that takes place not only in Latin America, but also in Africa and other parts of the developed world, Shannon said.