Muslim leaders in Bradford have said they fear a possible backlash against their communities after the bomb attacks in London.
Police boarded trains arriving at Sheffield station
Dr Abdul Barry Malik from the Ahmadiyya Muslim Association said he hoped people realised the bombings on Thursday were the acts of individuals.
Major faith groups in Yorkshire have united to condemn the attacks.
Meanwhile, North Yorkshire Police put extra officers on the streets. Rail services to London remain disrupted.
'Pitiless and unforgiving'
Dr Malik said Muslim communities had previously suffered when some young men were found to be associated with members of Al Qaeda.
But he said no minority group should be made a scapegoat.
"Years ago when we had some attacks on British cities by Irish terrorists we didn't blame the Christians as a whole or the Roman Catholics," he said.
"We should not blame all the Muslim communities."
Ishtiaq Ahmed, from the Bradford Council for Mosques, said the attacks had been senseless and indiscriminate mass murder.
"This is not Islamic and those who are, those who may be doing it under the name of Islam are not Muslims as far as I am concerned," he said.
In a joint statement Christian, Hindu, Muslim, Sikh and Jewish leaders in Bradford described the attacks as a "pitiless and unforgiving act of cruelty."
It added: "We take comfort from the characteristic good sense of Bradfordians and their refusal to concede to terrorists a victory of sowing fear and hatred between communities."
In Hull, community police officers and representatives from asylum support services have been visiting mosques and services for refugees and asylum seekers to reduce the fear of reprisals.
Hull City Council said: "It is their actions that give terrorists away, not their appearances.
"No community or religion can or should be made a scapegoat for the actions of terrorists."
In North Yorkshire, police patrols have been stepped up across the county.
A spokesman said that although no threat had been received "officers will be on the streets to provide residents with reassurance and advice."
Train services between Yorkshire and London are running but remain disrupted.
GNER has started running hourly services from King's Cross along the East Coast Mainline to Yorkshire.
A limited service run by WAGN is also operating between Peterborough and King's Cross.
A GNER spokesman said they hoped to increase service throughout the day and it could be almost back to normal by the evening.
Midland Mainline services between Sheffield and London St Pancras were restored on Thursday evening.