"You have prostituted your religion, poisoning the memory of your ancestors who suffered greatly," Bob James wrote in one tweet to her.
He also said: "I think Riley is using her influence as a popular celebrity to undermine the Labour party. Her method, though, using her Jewish heritage to promote self-interest, is appalling."
At another point, he said: "Riley has been open about her dislike of Corbyn… You have to hand it to the Tory party for getting her to risk her career for 30 pieces of silver."
In response, Ms Riley tweeted: "Are you an official Labour spokesperson, Bob, or just a big cheerleader?"
In response to the Mail on Sunday story, Mr James tweeted: "Its a good job I don't read sh*te like the Daily Hate mail."
The paper reported he denied being antisemitic when it contacted him.
A Labour spokesperson said: "We take all complaints of antisemitism extremely seriously and we are committed to challenging and campaigning against it in all its forms.
‘All complaints about antisemitism are fully investigated in line with our rules and procedures and any appropriate disciplinary action is taken."
