"That was not raised and not suggested. There was obviously a concern on the American side that they should retain the right to use military force if their planes were threatened or brought down or if the weapons controls exercised through the UN proved ineffective.
"But that was reserving the right to use force rather than any plan or threat to use force any greater than President Clinton's administration had used."
Sir John visited Washington in January 2001 before President Bush's inauguration for informal talks with the incoming administration.
The then UK prime minister Mr Blair and Mr Bush discussed Iraq at their first meeting at Camp David in February 2001, he said.
Sir John told the inquiry Mr Bush said at that meeting he wanted a more "realistic" policy on Iraq.
Sir John said Iraq was seen as a continuing - rather than growing - threat both to its neighbours and over what at the time was believed to be its development of weapons of mass destruction.
"The concern was that measures we had in place to contain the threat were increasingly difficult to sustain," he told the inquiry.
He said the feeling from the meeting between Mr Blair and Mr Bush was how to make the existing containment policy more sustainable, rather than "sharpen" it.
Options for regime change were considered, but these involved methods such as indicting Iraqi president Saddam Hussein for war crimes and trying to communicate to the Iraqi people the benefits of change.
He said a Whitehall policy review paper, approved by Mr Blair, recommended narrowing the scope of sanctions to weapons as well as goods that could be used in WMD programmes.
Sir John, the current head of MI6, became a special envoy to Baghdad in 2003.
He told the inquiry he found "serious disorder" when he arrived in Iraq.
"I was very disappointed by the quality of senior figures who were mainly retired Vietnam-era US generals," he said.
Sir John said he did not believe that disbanding the Iraqi army that year had been pivotal in provoking a Sunni insurgency.
The inquiry - headed by Sir John Chilcot and looking at events before, during and after the Iraq war, between 2001 and 2009 - was adjourned until Monday.
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