Lord Foulkes, the former UK minister who is now an MSP, sparked a heated row after he warned the Nationalists over their disparaging talk of "London Labour".
He claimed the SNP encouraged people "on the extreme outskirts of nationalism to think it is OK to do things that could be very harmful to English people".
However, Henry McLeish, the former Labour First Minister, launched a stinging attack on his party colleague over the remarks.
Mr McLeish said he was "very disappointed and saddened" by Lord Foulkes' comments.
"I think in Scotland at the present time there is no need for that type of vitriol for the SNP," he said.
A spokesman for the Labour party said neither Lord Foulkes nor Wendy Alexander, the party's leader-elect, would be apologising.
The two spoke by phone yesterday but no details of their conversation were released.
Lord Foulkes was unavailable for comment and Labour issued a one line statement in response to the continuing controversy.
The party spokesman said: "George Foulkes has made it clear that he is not accusing the SNP of racism".
According to Labour, the MSP had said: "I'm not suggesting for a second that the SNP are racist, or indeed, anti-English.
"What I am saying however is that Alex Salmond needs to be very careful when he makes snide remarks about 'London' Labour and the 'London' Government, that he's not fanning the flames of any existing anti-English sentiment.
"That would be deeply irresponsible".
A source close to Alex Salmond, the First Minister, said: "We would associate ourselves with the sensible, dignified remarks of Henry McLeish.
"It's a shame the Labour Party don't have the grace to apologise and draw a line under George Foulkes's antics.
"He has only succeeded in making himself look silly and his party look shabby."