National Security Adviser Mohammed Daoud said: "We had expected this from the terrorists at the beginning of Ramazan to shed the blood of the innocent ... We are ready to deal with the security situation this month."
The attacks in the Green Zone killed at least five people, including three American civilians, one Iraqi and wounded at least 18 when at least one suicide bomber and his colleague unleashed carnage in back-to-back blasts just before 1.00 pm.
The State Department in Washington put the death toll at four Americans and six Iraqis, but the US army in Baghdad and the embassy stuck to the lower number.
State Department Spokesman Richard Boucher said the dead Americans were security staff with a private company on contract to protect the US Embassy. He added that embassy staff had been ordered to remain in the heavily fortified facility until further notice.
A waiter, Abdul Razaq Mohammed, 32, said two men, aged around 25, one in a yellow shirt and the other wearing grey, sat and drank tea for 25 minutes at the popular Green Zone cafe. They were carrying black bags and in conversation said they were Jordanians.
Then one in the yellow shirt got up and walked away. Five minutes later an explosion shook the nearby bazaar, Mohammed said.
Then, within minutes, an explosion shook the restaurant.
The US military said it feared more attacks over the Ramazan period inside the area once considered safer than any other place in Baghdad.
Some 20 minutes later, the US military said planes had carried out air strikes on a suspected weapons storage facility and safe house in Fallujah for operatives of Zarqawi.
Two US soldiers were killed in bomb attacks on Thursday in Baghdad, raising the US military death toll in Iraq to 1,083, according to a Pentagon tally.