It was posted in Arabic late on Sunday on the Islamic discussion website www.myislah.org and dated 19 August, the day of the attack on the UN headquarters.
The statement's authenticity could not be verified. On Thursday, an Arabic television channel reported a previously unknown Iraqi group had claimed responsibility for the attack.
Written in heavily symbolic and oblique language, the statement was signed by Brigades of Abu Hafs al-Masri and followed by the words al-Qaida in parentheses.
It referred to a previous warning issued on 15 August in which it said it would "exhaust and confuse" America and its "henchmen".
"We meant that we would carry out such a lethal and surprising attack that the enemy will not know where, when and how we will strike," the statement said.
"So why the United Nations? Number one, the United Nations (is against Islam), it is a branch of the American State Department and it wears the robes of an international organisation.
"The double standard policies of the United Nations are against Arabs and Muslims ... It is clear like the light of the sun at midday"
"The double standard policies of the United Nations are against Arabs and Muslims. This issue does not need to be proved. It is clear like the light of the sun at midday," the statement said.
The statement called UN envoy to Iraq, Brazilian Sergio Vieira de Mello, "America's number one man".
Vieira de Mello was killed when a truck loaded with explosives blew up outside his Baghdad office on 19 August and some investigators have suggested he was an intended target.
The envoy, whose body has been returned to Geneva for burial, said he had received threats two weeks before the attack, according to the Lebanese newspaper, al-Mustaqbal, before his death.
In an interview with BBC Brasil the paper's editor, Fouad Hotait, said the remarks had been made off the record, but that after the bombing he felt obliged to reveal them.
Diaa Rashwan, an expert on Islamist groups at the Cairo-based al-Ahram Centre for Political and Strategic Studies, said al-Qaida had been using Internet discussion boards to distribute statements for about six months.
"The language and reference are in line with other al-Qaida statements," he said.
Washington accused al-Qaida of carrying out the September 11 attacks on the United States in 2001.
It was not clear if the name of the group issuing the claim was a reference to Muhammad Atif, also known as Abu Hafs.
The Egyptian was a close associate of Usama bin Ladin and was reported to have been killed in US military strikes on Afghanistan in December 2001 during the war to oust the Taliban and hunt down the al-Qaida members they sheltered.
The United States has blamed remnants of Saddam Hussein's regime for attacks in Iraq in the months since US President George Bush declared the war to oust the Iraqi leader over on 1 May.
But US officials have said a large number of foreign fighters were entering the country. Bush said last week that "al-Qaida-type fighters" were present in Iraq.