Brazil's sports minister Aldo Rebelo spoke to Blatter on the phone after the global football chief apologised in an open letter for comments made by FIFA general secretary Jerome Valcke.
Rebelo stressed Brazil's commitment to foster "cooperation and harmony with FIFA in preparations for the Cup " in a conciliatory statement issued after their phone call.
Blatter's written apology came one day after Valcke sent a similar letter to Rebelo apologising for saying Brazil's World Cup preparations were "not working" and that organisers needed "a kick up the backside."
Valcke's remarks caused uproar in Brazil, prompting the government to notify FIFA it would no longer accept the Frenchman as the world football governing body's point person for the 2014 World Cup.
Blatter's letter offered an "apology to all those who had their honour and pride wounded, especially the Brazilian government and President Dilma Rousseff."
He also asked to meet with Rousseff next week to personally discuss the standoff - and progress in Brazil's World Cup preparations - after a tour to Asia.
"We waste time over conflicts," Blatter wrote. "We must work together. We have a common goal: to organise an extraordinary World Cup in the country of football, the country of champions.
"Brazil deserves to host the World Cup and the whole world is anxiously waiting for that to happen."
Asked about Valcke's apology, Rebelo said he planned to reply in writing in the coming days.
Blatter's letter was delivered just hours before a congressional committee in Brazil finally agreed on the text of a crucial bill setting legislation for the World Cup.
