Netanyahu and his wife, Sara, will be staying in Rio until Tuesday, when they will fly to Brasilia for the inauguration.
Netanyahu had announced his trip to Brazil following a November 1 tweet from Bolsonaro indicating he intends to move the Brazilian Embassy in Israel from Tel Aviv to Jerusalem, following in Trump's footsteps.
JTA reported that Netanyahu may cut his five-day visit to Brazil short over the political developments in Israel. Bolsonaro said that "we are opening a new era in ties, and making history". "Israel is the promised land and Brazil is the land of promise".
Such a move by Bolsonaro would be a sharp shift in Brazilian foreign policy as it was for the United States when President Donald Trump relocated the USA embassy to Jerusalem in May.
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The leaders said that the talks initiated Friday will continue when Bolsonaro travels to Israel in 2019.
Netanyahu, calling his visit "historic", also spoke of "the brotherhood, the alliance" the two planned as something that "can carry us to great heights". He said that for his country to overcome obstacles, "we need good allies, good friends, good brothers, like Benjamin Netanyahu".
"I am certain that the Secretary and the President-elect will discuss the human rights", the State Department official told reporters. Brazil has traditionally backed a two-state solution to the Israeli-Palestinian conflict. Trump has urged countries to follow national interests in economic, security, foreign relations and environmental policies.
The official, who was not authorized to preview Pompeo's trip publicly and spoke on condition of anonymity, said Pompeo would raise the broad issue of sovereignty when discussing multilateral agreements like the Paris climate accord from which Trump has said the US will withdraw.
He will also hold talks with the presidents of Chile and Honduras while there, among other officials, and meet with members of the Jewish community and a pro-Israel Christian group. Brazil-Israel trade now amounts to $1.2 billion.