There was no evidence of any serious co-operation between Saddam Hussein's regime and al-Qaida after the 9/11 attacks, and contacts before had been sporadic, senior civil servants told the Iraq war inquiry in London today .

Iraq did not want to be associated with the attacks and was not a natural ally of the terrorists, the civil servants said, as they confirmed that Baghdad was not "top of the list" when it came to concerns over weapons capacity in 2001; Iran, Libya and North Korea were considered greater threats.

Saddam Hussein's regime was not a natural ally of al-Qaida, the Chilcot inquiry has been told. (Photograph: Awad Awad/AFP/Getty Images) However, one of the witnesses said he was not surprised by the notorious claim in the government dossier to justify the 2003 invasion that Iraq could deploy weapons of mass destruction within 45 minutes.

Tim Dowse, the head of counter-proliferation at the Foreign Office at the time, and Sir William Ehrman, who was its director of international security at the same department, were giving evidence on the second day of the hearings.

Saddam had supported Palestinian terrorists but his regime's contacts with groups linked to al-Qaida were sporadic, Dowse said. "There had been nothing that looked like a relationship between the Iraqis and al-Qaida. In fact, after 9/11 we concluded that Iraq actually stepped further back. They did not want to be associated with al-Qaida. They weren't natural allies.

"Speaking personally, when I saw the 45 minutes report, I did not give it particular significance because it didn't seem out of line with what we generally assessed to be Iraq's intentions and capabilities with regard to chemical weapons."

He took the 45-minute claim to refer to a multi-barrelled rocket launcher kept ready for deployment by Iraqi forces in the event of conflict.

"It certainly took on a rather iconic status that I don't think that those of us who saw the initial report really gave – it wasn't surprising," Dowse said.

Asked about suggestions that the 45 minutes referred to a possible WMD strike against another nation, Dowse said: "I don't think we ever said that it was for use in a ballistic missile in that way." The inquiry panel member Professor Sir Lawrence Freedman replied : "But you didn't say it wasn't."

Yesterday, other officials said Tony Blair's government had known prominent members of the Bush administration wanted to topple Saddam years before the invasion. But the Blair government initially distanced itself from the idea, knowing it would be unlawful.British intelligence dismissed claims by elements in the US administration that the Iraqi leader was linked to Osama bin Laden, the inquiry heard.

Evidence given at the opening day of the inquiry, chaired by the former top civil servant Sir John Chilcot, painted a picture of a Whitehall slowly realising the significance of George Bush's election in November 2000 on US policy towards Iraq.

Sir Peter Ricketts, a former chairman of the joint intelligence committee (JIC) and now the Foreign Office's top official, told the inquiry that even before Bush came to power, an article written by his then national security adviser, Condoleezza Rice, warned that "nothing will change" in Iraq until Saddam was gone.

Sir William Patey, then head of the Middle East department at the Foreign Office, said: "We were aware of these drumbeats from Washington and internally we discussed it. Our policy was to stay away from that part of the spectrum."

Patey revealed that in late 2001 – after the 9/11 attacks on the US – he asked officials at the ministry to draw up an Iraq "options" paper including regime change. "We dismissed it at the time because it had no basis in law," Patey told the inquiry.

Simon Webb, a former policy director at the Ministry of Defence, described the issue of regime change in Iraq during the early days of the Bush administration as "the dog that did not bark. It grizzled, but it did not bark."

The exchanges on the opening day of the inquiry were significant in the light of previously leaked documents revealing Blair told Bush in April 2002 – nearly a year before the invasion of Iraq – that he would in principle support military action "to bring about regime change".

A month earlier, David Manning, a Downing Street foreign policy adviser at the time, told Blair that he had advised Rice that "you [Blair] would not budge in your support for regime change but you had to manage a press, a parliament, and a public opinion which is very different than anything in the states".

Yet in July 2002, Lord Goldsmith, then attorney general, was still warning the government that regime change was "not a legal basis for military action", according to leaked documents.

Pressed by Sir Roderic Lyne, a member of the inquiry panel and a former UK ambassador to Moscow, to explain the JIC's assessment of the threat posed by Iraq at the time, Ricketts replied that it was a "major feature on the agenda but by no means dominant".

The Balkans, Sierra Leone – where British forces were facing down rebels – and Afghanistan were considered higher priorities, though attempts by Saddam to get his hands on weapons of mass destruction were "a continuing threat", Ricketts added. Patey said Iraq did not pose "an immediate threat".

The Iraq inquiry heard that any lingering US sympathy for Britain's policy of "containment" of Saddam through UN sanctions quickly evaporated after 9/11. The Pentagon, rather than the US state department, became the "dominant instrument" in US foreign policy.

Moreover, voices in Washington were starting to link the Iraqi leader to al-Qaida. Ricketts said Britain had no evidence showing Iraq was "linked in any way to 9/11 ... We didn't have any such evidence."

Neo-conservatives in the Bush administration and the CIA claimed in the run-up to the invasion that Saddam was linked to al-Qaida, a claim dismissed at the time by MI6.

According to previously leaked documents, Ricketts, the political director at the Foreign Office at the time, described the US in 2002 as "scrambling to establish a link between Iraq and al-Qaida", a link that was "so far frankly unconvincing". He told Jack Straw, then foreign secretary: "We have to be convincing that the threat is so serious/imminent that it is worth sending our troops to die for. Regime change does not stack up. It sounds like a grudge match between Bush and Saddam."

Lyne questioned why Britain and the US came to such different conclusions from other countries about the dangers Iraq posed. He asked: "With the exception of Kuwait, were the countries in the region banging on doors in London and Washington saying 'We're very worried about Saddam Hussein, please can you do something about him?'"

Patey replied: "I can't say my door was being knocked on very regularly."

One of the panel members, Lady Prashar, later questioned whether official policy towards Iraq was about disarmament or regime change.

"It seems a deliberate policy of ambiguity," she said.

"I don't think that's true," replied Ricketts.