The Government and Muslim communities both had to do more as they step up the "battle of hearts and minds" against Islamic extremism, Community Secretary Ruth Kelly said yesterday.

The news came as Home Secretary John Reid said a terrorist attack on Britain is highly likely but no longer imminent.

The level was downgraded from critical to severe after intelligence experts at the Joint Terrorism and Analysis Centre decided that the immediacy of the threat had passed.

Passengers endured yet another day of airport disruption yesterday despite an easing of the anti-terror procedures.

And airport operator BAA continued to be the focus of airline anger over the delays and cancellations which have crippled schedules over the last few days.

Speaking after more than three hours of talks with Muslim leaders Ms Kelly acknowledged there were "different views" over aspects of Government policy.

There had been a series of "sharp and challenging exchanges" which had been "very constructive and forward looking", she said.

"There is a battle of hearts and minds to be won within the Muslim community, working with the Muslim community to take on the terrorist and extremist elements that are sometimes found within it, not just in the Muslim community, but elsewhere as well."

Ms Kelly said she had discussed ways of making sure that if there was frustration, there were "democratic channels for that to be vented".

Since the most recent terror arrests, the Government and Muslim leaders were trying to boost the more relevant aspects of the action plan drawn up in the wake of the July 7 attacks, she added.

She said: "We have all got to step up to the challenge.

"We have got to work together.

"Yes, the Muslim community has got to do more, yes we as Government have got more to do."

She was joined during the meetings by Deputy Prime Minister John Prescott and Communities Minister Meg Munn.

Muslim leaders leaving a series of meetings said they had agreed with Ministers on the need for a "partnership approach".

Dr Syed Aziz Pasha, secretary general of the Union of Muslim Organisations of the UK and Ireland, said: "We are willing to cooperate but there should be a partnership."

Asim Siddiqui, chairman of the City Circle network of Muslim professionals, said there appeared to be an "impetus" to deliver what had been proposed in the aftermath of July 7.

"Clearly there is a need for far greater Government focus in terms of time, attention and resources.

"What I mean by that is new money targeting at a grassroots level the very good work which is taking place up and down the country."