The police have increased their presence in areas with Muslim populations in the UK to deter attacks after the latest terror arrests.
It was "totally wrong" to retaliate against Muslims, Mr Fahey said|
Officers are investigating a small fire at a mosque in Chester but say it is too early to say whether it was in response to the alleged terror plot.
The small blaze was quickly extinguished and no-one was injured.
The head of the Muslim Council of Britain said Muslims were "fully behind" efforts to prevent attacks.
Dr Mohammed Abdul Bari said the community supported curbs on terrorism, but warned of "a distance" growing between them and the police.
Peter Fahey, the communities and diversities spokesman for the Association of Chief Police Officers (ACPO), said forces would be "very alive" to any threats.
He added that he was aware that there was a distrust among the Muslim community.
"It is something that we take very very seriously and we are working all the time to break that down," he said.
Dr Bari warned police must be very careful, as the failed raid in east London in June created "a distance" between them and Muslims.
"The people that I have been listening to - the old, young, men and women - they are saying that they are fully behind the police when it comes to national security and the public safety," he said in an interview with BBC Radio Leeds.
Dr Bari is to meet worried Muslims in West Yorkshire on Friday|
He called on his community to "work together" with detectives, saying: "This is our society and we could have been victims as well, so there is no second thought on that."
In June, Dr Bari warned that trust between the Muslim community and police could be damaged following the raid on a house in Forest Gate.
A Muslim man was shot in the shoulder and was arrested along with his brother.
Both were later released without charge and the police watchdog, the Independent Police Complaints Commission, judged the shooting to have been accidental.
Home Secretary John Reid has urged people of all communities and religions in the UK to join together to overcome "those who wish to harm us".
For four years we've been seeing more and more innocent people being harassed and demonised |
Fahad Ansari, Islamic Human Rights Commission
However, police "need to do a lot more thinking" before that can happen, argued Fahad Ansari from the Islamic Human Rights Commission, because their intelligence was "flawed".
"For four years we've been seeing more and more innocent people being harassed and demonised," he told BBC Radio 4's Today programme.
"We've seen very few terrorists being captured but a lot of innocent people destroyed.
"The more you alienate a community, it's not going to be good for future relations."
Muhammad Abul Kalam from the Muslim Safety Forum said that there was generally an increase in Islamophobic attacks following events such as Thursday's raids, in which 24 people were arrested.
"We simply don't want to see any kind of backlash unleashed against ordinary Muslims because of what has happened."
He said he believed his organisation had received no contact so far from the Metropolitan Police, despite having an ongoing advisory role for the security services.
"We'd like them to open those channels of communication and talk to them so that we can reassure the community leaders we speak to," he told BBC News.
Two Muslim brothers were arrested in the raid in Forest Gate in June|
Leading human rights lawyer and chair of the Muslim Council of Great Britain's legal affairs committee Khalid Sofi told BBC News the Muslim community had felt "shock and disbelief" at the arrests.
Mr Sofi said if the security services had indeed disrupted a genuine terrorist plot this would be very welcome, but it was important any evidence against the suspects was presented to their lawyers as soon as practically possible.
"Due to the international dimension to this case, it may take more time to assemble evidence," Mr Sofi said.
He is also concerned the enormous media coverage may have created an adverse impression of the suspects.
Meanwhile Khalid Mahmood, the Labour MP for Birmingham Perry Barr, said he accepted that young Muslims disagreed with the government's policy on terrorism, and this could lead to a minority turning to being led astray.
Some young people were being "sectioned off" and "brainwashed", he added.
And on occasions, "very new converts to the religion" did not have "a fundamental understanding of their own religion", he said.
But the Archbishop of York, Dr John Sentamu, said he did not believe that Islam was the real cause of any terrorist plots.
"Most of them are doing it because they are alienated, because they have been given a vision which is so imaginatively wicked that they believe we can build a better world than actually exists," he claimed.
A spokesman for Islamic political organisation Hizb ut-Tahrir said he would "urge caution before jumping to conclusions" about the 24 people arrested over the latest alleged terror plot.
"We hope there is no repeat of the media hysteria and police leaks that followed the Forest Gate raids when reports of 'chemical vests' and 'bomb factories' turned out not to be true," said Imran Waheed.