The boast comes only hours after a 19-year-old UK teenager from Essex was arrested and accused of being part of the hacker group.
In a tweet in the early hours of Wednesday morning, LulzSecBrazil wrote: "TANGO DOWN brasil.gov.br & presidencia.gov.br"
Another Twitter message from the main LulzSec page then added: "Our Brazilian unit is making progress. Well done @LulzSecBrazil, brothers!"
The websites are the official pages of the Brazilian Government.
Attempts to access the websites this morning proved unsuccessful and the attacks appeared to have swamped the pages with internet visits, causing them to crash.
And as more details of LulzSec emerge it is becoming clear that this is a group with sinister intent.
Yesterday, the group posted the private details, including the home addresses, of one hacker and his associate who 'tried to snitch on us'.
They added: “There is no mercy on The Lulz Boat. Snitches get stitches.”
LulzSec's previous targets have included the CIA, the US Senate, the US television broadcaster PBS, Britain's Serious and Organised Crime Agency and the technology firms Sony and Nintendo.
Ryan Cleary, 19, the son of a college lecturer was arrested last night accused of being a “major player” in LulzSec.
He was held in a raid at his family home in Wickford following a joint investigation between Scotland Yard and the FBI.