Dana Perino, the White House spokeswoman, declined to comment on the claims made in The War Within: A Secret White House History 2006-2008, Woodward's fourth book on the administration of George Bush, the US president.
"We have extensive co-operation with Prime Minister Maliki. Our ambassador sees him almost daily," Perino said.
"To the extent that they [the Iraqi government] have any concerns, because we have the good relationship that we have with them ... I'm sure that they'll be talking about it."
Woodward's book asserts that the surveillance of the Iraqi prime minister caused concern among several senior US officials, who questioned whether it was worth the risk given Bush's efforts to earn al-Maliki's trust, the Washington Post reported.
The book also questions whether the US troop build up ordered by Bush in 2007 and known as the "surge", was not the primary reason for a drop in violence in Iraq.
Instead Woodward says it was only a factor alongside others such as the emergence of the Sunni Awakening forces and the decision by Muqtada al-Sadr, the Iraqi Shia leader, to rein in his al-Mahdi Army.
Stephen Hadley, Bush's national security adviser,
issued a sharply worded statement countering a number of claims made in the book but his statement said nothing about Woodward's assertion that the Bush administration spied extensively on Iraq.