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."
It was not clear if Rousseff would meet with Blatter next week, when Valcke is also scheduled to visit Brazil to tour construction sites in some World Cup host cities.
Valcke, who has irked Brazilian officials in the past, claimed in his letter to Rebelo that translators misinterpreted his words in his native French. But reporters who heard his comments said he spoke in English.
Asked about Valcke's apology, Rebelo said he planned to reply in writing in the coming days.
Brazil is struggling to prepare for the World Cup and its curtain raiser, the 2013 Confederations Cup. Stadium construction was slow to get started and costs have ballooned. More worryingly, vital infrastructure projects such as hotels, roads and airports are way behind schedule.
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.
The bill, called the World Cup Law, will now go to a plenary session in the lower house of Congress before going to the Senate.
Lawmakers have delayed passing the bill, and the government has clashed with FIFA repeatedly over whether alcohol should be sold inside stadiums and over which groups are entitled to discounted tickets.
A few protesters unfurled anti-FIFA banners as the debate took place.
