The statement also vowed more attacks on occupation targets.
"We give you good tidings ... your brothers with their boats targeted oil tankers in Mina al-Amiq and Mina al-Bakr," said the statement signed by al-Zarqawi and published on Muntada al-Ansar Islamist website.
Basra terminal, previously known as Mina al-Bakr, accounts for 85% of Iraq's crude exports.
Three US navy sailors died in the attack by bombers in three boats who blew themselves up in and around the Basra terminal zone, one of the most heavily guarded facilities of its kind in the world.
Al-Zarqawi is widely believed to be in Iraq.
It was not immediately possible to verify the authenticity of the statement posted on the website, which has previously carried statements attributed to Usama bin Ladin's network.
The statement compared the attack on the Basra terminal to the bombing in 2000 of the US warship Cole in Yemen's Aden port which killed 17 US sailors and which was blamed on al-Qaida.
"As what your brothers, the al-Qaida lions did to the destroyer Cole in Aden port, they have repeated this attack in a new garb and with stubborn determination by striking vital economic links of the infidel and atheist states which came to raise the Christian banner in Muslim countries," it said.
"We tell you enemies of God, robbers of oil and riches and drug traders ... O snakes of evil, we will exterminate and debilitate you by land, sea and air until God makes us victorious or until we die," the statement added.
"We tell you enemies of God, robbers of oil and riches and drug traders ... O snakes of evil, we will exterminate and debilitate you by land, sea and air until God makes us victorious or until we die"
Statement attributed to Abu Musab al-Zarqawi
Iraq is almost completely dependent on the Basra terminal to provide revenue. Iraqi and US occupation officials said southern oil infrastructure remained secure despite the thwarted attacks and oil exports from Basra terminal had resumed on Sunday.
The statement mentioned a visit to Iraq by Australian Prime Minister John Howard on Sunday to see some of Australia's troops.
The statement said the "wicked" Australian prime minister, a firm US ally, "rushed" to the site of the boat attack to "see what happened to his troops".