Still, some American officials worried that Brazil was not taking the threat seriously enough. Trying to avoid taking sides in foreign conflicts, including those in the Middle East, has been a pillar of Brazilian foreign policy. Some political leaders here contend that doing so could make Brazil a target for Islamist militant groups.

But the assessment of Brazil’s vulnerability began to change around the end of last year, American officials and Brazilian security analysts said, as the Islamic State continued to show that it could carry out and inspire attacks in different parts of the world.

“The changing nature of attacks around the world and the realization that Brazil is vulnerable with the proximity of the Olympics have been pushing the government to rethink its approach,” said Marcos Ferreira, a scholar at the Federal University of Paraíba who focuses on terrorism in South America.

In March, President Dilma Rousseff signed antiterrorism legislation that enhanced the government’s authority to arrest and jail people suspected of planning attacks. Human rights groups criticized the law as being too broad, but Ms. Rousseff, a leftist who was imprisoned as a youth over her involvement in a guerrilla group resisting the military dictatorship, signed the law despite fears that it could be used to infringe on civil liberties.

“There is increasing awareness in Brazil of the threat of terrorism, and we are pleased that Brazil passed a new counterterrorism law in March,” said Liliana Ayalde, the American ambassador to Brazil. “The legislation has opened up new channels of cooperation between our two governments.”

The passage of the law — along with the increased intelligence sharing between Brazilian and American officials — unfolded here at a time of political upheaval. Ms. Rousseff, who is now facing an impeachment trial, was trying to fend off opponents’ attempts to topple her. Her vice president, Michel Temer, emerged victorious in the power struggle. As interim president, he is now waiting to see if the Senate definitively ousts Ms. Rousseff in an impeachment trial on charges of budgetary manipulation.

But the political turmoil did not seem to affect Brazil’s preparations for threats around the Olympics. Officials from both countries who had been interacting with one another said they continued to do so despite the changes in the upper echelons of government.