The resignation of the commander of US forces in Iraq and Afghanistan does not signal a policy change on Iran, US Defence Secretary Robert Gates says.
Adm Fallon reportedly called the Esquire article "poison-pen stuff"
Admiral William Fallon said on Tuesday he was stepping down because of public perceptions of a rift with Mr Bush.
A recent article said Adm Fallon opposed military strikes against Iran.
The Pentagon also denied claims by leading Democrats that the resignation was a sign of White House attempts to stifle dissent.
The affair centres on an article in the April edition of Esquire magazine which described the admiral as "the strongest man standing between the Bush administration and a war with Iran".
But Mr Gates said there were no significant differences between the views of Adm Fallon and the Bush administration's policy on Iran.
Adm Fallon oversaw US operations in Iraq and Afghanistan
He said the idea, suggested in the article, that Adm Fallon's departure would indicate that the US was planning to go to war with Iran was "ridiculous".
Adm Fallon said he did not believe there had "ever been any differences about the objectives of our policy", and was quoted by the Washington Post as describing the article as "poison-pen stuff".
But Esquire's editor-in-chief, David Granger, said the magazine stood "four-square behind the story".
He said Adm Fallon's resignation and its aftermath bore out the magazine's "reporting on the critical issue of tensions between US Central Command and the White House over Iran policy".
Leading Democrats expressed fears of attempts by the White House to quash dissent.
"I am concerned that the resignation of Admiral William J Fallon... is yet another example that independence and the frank, open airing of experts' views are not welcomed in this administration," Senate Majority Leader Harry Reid said.
But defence department press secretary Geoff Morrell said "people should not misconstrue this as the price to be paid for speaking out within the Pentagon".
He said the issue had been "a perception problem that dogged Admiral Fallon - this perception that he was in a different place than the president and the administration when it came to Iran".
Adm Fallon became head of the US Central Command - which covers an area from the Horn of Africa into central Asia and includes responsibility for US operations in Iraq and Afghanistan - a year ago.
The admiral released a statement through Central Command's Florida headquarters on Tuesday.
He cited the "embarrassing situation and public perception of differences between my views and administration policy" as his reason for retiring.
"I don't think that there really were differences at all," said Mr Gates, referring to the perceived schism between Adm Fallon and the Bush administration over Iran policy.
Responding to the resignation, Democratic presidential hopeful Hillary Clinton urged the Bush administration to pursue diplomacy with Tehran instead of conflict.
The New York senator described the admiral as a "voice of reason in an administration which has used inflammatory rhetoric against Iran".
President George W Bush said Adm Fallon deserved "considerable credit for progress that has been made... in Iraq and Afghanistan".
But Adm Fallon's resignation is richly suggestive of discord at the top between the military and the White House, says the BBC's Adam Brookes in Washington.
Adm Fallon's comments - that included telling Arabic TV station al-Jazeera last year that "I expect there will be no war (with Iran)" - incurred the wrath of the Bush administration, says our correspondent.
Observers say the resignation comes at a time when the US administration seems to be struggling on a number of fronts to maintain the international pressure on Iran, not least with the recent US National Intelligence Estimate that suggested Iran had had a nuclear weapons programme but halted it in 2003.
The Bush administration's official policy towards Iran is to use diplomatic and economic pressures to resolve differences while retaining the possibility of military options.
The US and other Western nations suspect Iran is using its nuclear programme to develop atomic weapons - a charge Tehran denies.