In a letter to Ruth Davidson, the SNP leader said the remarks attributed to an unnamed member of the Tory communications team were “completely unacceptable” and called on her to publicly withdraw them on behalf of her party.
The row began earlier this month after Christian Allard, the French-born former SNP MSP, reported Tory MSP Alexander Burnett to the Standards Commissioner for failing to disclose his business interests when raising objections against a rival property developer in the Scottish Parliament.
Ms Sturgeon described it as a “serious issue” and called for Ms Davidson to apologise during First Minister’s Questions last week, but the Tory leader has yet to respond.
Now, in an escalation of the row, the SNP leader has written to her political rival suggesting that a failure to apologise would set a bad example following a reported rise in xenophobic hate crimes in the wake of the EU referendum.
It followed a satirical "rap-off" involving members of the group Whitsherface pretending to be Ms Davidson, Labour leader Kezia Dugdale, First Minister Nicola Sturgeon and Nationalist MP Mhairi Black.
When footage of the skit at St Luke's in Glasgow appeared on social media it provoked a storm of criticism.
“But those reassurances risk being undermined when you, as Scottish Conservative leader, fail to retract or apologise for the offensive remarks issued by your office.” As well as calling on Ms Davidson to condemn, retract and apologise for the remarks, the First Minister asks her to make clear that EU citizens living in Scotland “have a right to involve themselves in the affairs of their communities and in public life in general”.
Last week the party’s head of communications said the original statement was not intended to be offensive, but conceded that it was open to misinterpretation.
He also denied that anyone in the party was xenophobic.