SÃO PAULO—Fitch Ratings downgraded Brazil’s sovereign credit rating on Thursday, leaving the country at one notch above junk status as President Dilma Rousseff faces a standoff with Congress while she struggles to get the country’s finances in order.

Fitch cited the rising government debt burden and a worsening political and economic situation, and left its negative outlook for the country in place. Earlier Thursday, before the downgrade was announced, Rafael Guedes, director of Fitch Ratings in Brazil, said a negative outlook...