The posting attributed to the group named the attackers as Mohammed al-Ghaith and Abdullah al-Tweijri - both on a list of top wanted militants - and said Friday's attack was in response to a call by al-Qaida leader Osama bin Laden to target oil installations.
"We shall not cease our attacks until our territories are liberated," said the statement, adding that the operation was successful and that some attackers got away.
It said the attackers were able to get through two gates and blew themselves and their vehicles up as planned, rejecting Saudi state media reports that security forces stopped the attackers.
"We renew our vow to crush the forces of the crusaders and the tyrants and to stop the theft of the wealth of the Muslims," said the statement signed by al-Qaida in the Arabian Peninsula.
The authenticity of the statement, posted on a web site often used by Islamist groups in Iraq, could not be verified.
Militants on Friday attacked the Saudi Arabian oil facility at Abqaiq, blowing up cars packed with explosives at the gates after being fired upon by security guards.
At least four attackers and two security guards were reportedly killed in the attack.
Abqaiq handles crude pumped from the giant Ghawar field and ships it off to terminals Ras Tanura, the world's biggest offshore oil loading facility, and Juayma.
It also pumps oil westwards across the kingdom to Red Sea export terminals.