The Illinois senator pledged to work side-by-side with the rest of the world on issues like nuclear proliferation, poverty, economic development in Latin America and the violence in Darfur.
"While we're at it," he said, "we're going to close Guantanamo. And we're going to restore habeas corpus. ... We're going to lead by example - by not just word but by deed. That's our vision for the future."
Habeas corpus is a tenet of the Constitution that protects people from unlawful imprisonment.
The White House said Friday that Bush has made closing the prison in Cuba a priority and that Bush's top aides are in active discussions about the subject.
Obama, his white shirt sleeves rolled up, spoke for roughly 30 minutes in the muggy heat to a crowd his campaign estimated at about 1,000 people. It was the first-term senator's first visit to San Antonio since declaring that he would run for president. Many in the crowd wore blue "AlamObama" T-shirts playing off the city's famous landmark, the Alamo.
Obama said, "There's one thing that we can still get right in (the Iraq) war," which is to commit to treating troops returning to the U.S.
"When our young men and women have served this country, I don't care if you were for the war or against the war, but they have served our country. They have done every single thing that we have asked of them, with bravery and valor, they should not have to beg when they come home to get the services they need," Obama said.
The San Antonio area is home to several military installations, including Fort Sam Houston and its Brooke Army Medical Center, where many soldiers are sent for treatment.