The Brazilian government has in effect blocked Israel's next selection for ambassador from taking up his post, because he was the leader of a settler organization in the West Bank.
Dani Dayan served as head of the Yesha Council of Jewish settlements from 2007 to 2013 and lived in Maale Shomron, a settlement nearly 20 miles east of Tel Aviv.
Israel announced his appointment as the next ambassador to Brazil in August, but the diplomatic standoff began only this month after the previous ambassador left the country and Brazil failed to issue a formal acceptance for Dayan.
Three dozen organizations allied with Brazil's Workers' Party, to which the president belongs, have signed a petition asking her to deny Dayan his diplomatic credentials.
Rousseff may have limited political power to resist those demands even if she wanted to, because she is facing impeachment proceedings based on accusations that her government broke fiscal responsibility laws and she cannot afford to alienate her allies.
Brazil and Israel have had a testy relationship in recent years.
In 2014, Rousseff temporarily recalled Brazil's ambassador to Tel Aviv over what she called "disproportionate use of force" by Israel in a military offensive in the Gaza Strip.
In response, an Israeli government spokesman called Brazil a "diplomatic dwarf" on the world stage.
Rousseff has also spoken against the settlements.
"We can no longer delay the creation of a Palestinian state coexisting peacefully and harmoniously with Israel," she said at the United Nations in September. "In the same vein, the expansion of settlements in the occupied territories cannot be tolerated."
Since 2010, Brazil has recognized the state of Palestine along the so-called 1967 borders.
Dayan — who is not related to Moshe Dayan, the former Israeli military leader and politician — was born in Argentina and moved to Israel with his family at 15. He is considered a moderate among settlers and has been a vocal critic of violence by Jewish extremists.
But he opposes creation of a Palestinian state. In a 2013 interview, he called the two-state solution "an invitation to war."
Israeli officials said they will continue to push for Dayan.
"The Foreign Ministry will use all the tools at its disposal," Tzipi Hotovely, the deputy foreign minister, said in a statement. "The state of Israel will not accept the disqualification of an ambassador for his ideological background."
Those efforts would include summoning the Brazilian ambassador in Israel, reaching out to the Jewish community and lawmakers in Brazil, and downgrading Israeli diplomatic representation in Brazil to "secondary level," she said.
In an interview with the Brazilian newspaper O Globo this week, Israel's honorary consul in Rio de Janeiro, Osias Wurman, compared the rejection of Dayan for being a settler to the forced bearing of yellow stars during the Nazi era in Germany.
Calling the situation a "total train wreck," the Times of Israel suggested this week that Dayan should be appointed consul general in Los Angeles, a "highly coveted post" that would allow him to save face.
Dayan said part of the responsibility for the impasse rests with Israel for mismanaging the situation.
"There were those in Jerusalem who thought that it would be good to sit it out and wait for things to work out," he said in an interview on Israel's Channel 2 this week. "They were wrong."
"Now the government must grab the bull by the horns and address the real issue, which is whether or not it will allow a settler to be disqualified," he said. "I am positive the Foreign Ministry will know what to do."
Special correspondents Rigby and Sobelman reported from Belo Horizonte and Jerusalem, respectively.