The political race row re-erupted on Monday after Lib Dem leader Charles Kennedy said the language the Tories used on asylum was creating "a very unhelpful atmosphere indeed".
" For the Liberal Democrats to try and make politics out of what has been happening in Oldham is very regrettable "
Mr Kennedy backed his home affairs spokesman, Simon Hughes, who on Sunday said Mr Hague's words could be used to justify "intolerant behaviour".
The Tory leader hit back, saying the Lib Dems were seeking to gain political advantage over the issue.
Mr Hague said: "For the Liberal Democrats to try and make politics out of what has been happening in Oldham is very regrettable.
"I think they should stop doing that and they should apologise for doing so."
Mr Kennedy rejected the call for an apology, saying the Conservatives ought to apologise themselves for their "opportunist, knee-jerk response" to the issues of immigration, asylum and race relations.
He said: "They are the people who started this and I think they would do well to let the matter rest in the context of this election."
Shifting the blame
Meanwhile Home Secretary Jack Straw has sided with the Tories, accusing the Liberal Democrats of trying to shift the blame onto political opponents.
Mr Straw told BBC News: "I've always objected to this kind of moral relativism which seeks to shift the blame for criminal activity, from those actually causing it, to others."
His disagreement with the Tories over asylum was "completely separate" to the racial tension in Oldham, he said.
Another government minister, Michael Meacher, also sought to distance the election from the rioting - saying it was sparked by "provocative" racist incidents last week.
Mr Meacher, who is standing again to be an Oldham MP, said the atmosphere in the town had been aggravated by National Front incursions and the mugging of a 76-year-old white pensioner.
Prime Minister Tony Blair insisted on Monday that the Oldham riots were "not typical" of the state of British race relations.
Speaking on Teesside, Mr Blair expressed his "total and complete support of the police, because it is absolutely unacceptable that they are subject to this type of attack".
Sunday's rioting came after more serious violence on Saturday, in which up to 500 Asian youths battled against lines of riot police.