When he arrived in Iraq after the war, he said the situation was far worse than he feared and that "Baghdad was held together by chicken wire and chewing gum".
Maj Gen Cross said it was "too common" for the UK to blame the US for failings to stabilise the country after Saddam Hussein was toppled.
At a meeting at No 10 in February 2003, he said he conveyed his concerns to the prime minister about the lack of post-war planning in both the US and UK.
Mr Blair was "engaged", Maj Gen Cross said, but he claimed he got the sense there was "no coherent, single focus" across the government for post-war planning, nor any clear policy direction.
"I do remember saying, in so many words, I have no doubt at all that we will win this military campaign. I do not believe that we are ready for post-war Iraq."
He said he briefed officials in the run-up to the invasion that the chances of military action leading to chaos in Iraq were "not insignificant".
But in the most strident criticism of UK attitudes to post-war planning heard to date at the inquiry, he said he did not believe the issue was taken "sufficiently seriously" in Whitehall.
The team set up within the Foreign Office to focus on post-war planning happened "very late", he said, while consideration of the aftermath was hampered by a belief within sections of the British government that the invasion would not happen.
November-December: Former top civil servants, spy chiefs, diplomats and military commanders to give evidence
January-February 2010: Tony Blair, Gordon Brown and other politicians expected to appear before the panel
March 2010: Inquiry expected to adjourn ahead of the general election campaign
July-August 2010: Inquiry expected to resume
Report set to be published in late 2010 or early 2011
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