The missives singled out the former leader of the city’s Conservative group, Nadeem Ahmed, for particular ire.
“As a devout Christian, we cannot allow Muslims to take over,” one of the letters suggested.
The notes – sent to councillors Steve Tulley, Michael Graham, Betty Rhodes and Olivia Rowley – were all signed off by “a Conservative colleague”, although the party has said none of its members were responsible for the letters.
Councillor Tulley said: “I was sickened when I opened and read through it. It’s vile to be honest.”
Referring to the killing of MP Sir David Amess in his Essex constituency on Friday, he added: “Letters like this pale into insignificance but this kind of hate being directed at people who are trying to serve the public – of course it makes you uneasy and of course it will put people off getting into politics.”
He said that all four letters had now been passed to West Yorkshire Police which said it was investigating them for malicious communications.
Conservative group leader Nic Stansby said she was upset to hear about the letters.
"I was really shocked and disgusted by it," she said. "It certainly wasn't sent by any of our councillors.
"I've had abuse myself and no-one should have to put up with receiving letters like that. It's just not on."
Councillor Ahmed was ousted as leader of city’s Tories in August despite leading them to their best election results in years in the spring.
While no official reason has been given for his forced resignation, it is thought his centrist world view and willingness to work across the aisle did not always make him popular with right-wing members of his own party.
Responding to the letters, he said: “If someone doesn’t like me because of my politics, I take that on the chin. But trying to sow this kind of hate because of race or religion or sexuality or anything like that, it’s pathetic and it does need addressing. People who send things like that, they have nothing better to do. They need to get a life.”