Police are advising people to go about their daily lives but remain vigilant as they spoke about the measures in place to tackle a "despicable" anti-Muslim campaign.
Senior officers in Scotland told how they are taking the issue seriously and have committed a "substantial" police response to dealing with it.
It comes as officers and MSPs moved to reassure members of Scotland's Muslim community about the action taken so far against a social media and letter campaign urging people to "punish" a Muslim.
A community representative has said the campaign has already triggered Islamophobic incidents in Scotland.
The police officers set out their response at a meeting on Tuesday evening with the Scottish Parliament's cross-party group (CPG) on tackling Islamophobia, chaired by Labour MSP Anas Sarwar.
Describing the hate campaign as "despicable", Police Scotland's Superintendent David Pettigrew told the meeting at Holyrood that none of the letters have been received in Scotland.
He said: "There is no information available to us at this time to suggest there is any increased risk to the Muslim community.
"We review that constantly and we're in constant communication with our colleagues down south."
He said people should report any incidents but said they should not be scared to continue their everyday business.
"Always be vigilant and aware of your surroundings, but go about your daily business," he told the audience.
The officer spoke after hearing questions and concerns from a number of community leaders and representatives.
Deputy Chief Constable Johnny Gwynne told the meeting: "We can reassure you there is a substantial police response behind this.
"We are taking this seriously."
He added: "There is no intelligence of any direct threat to anybody in Scotland.
"We're as prepared as we can be in the absence of any specific detail.
"Our job is to stop that cancer in life which is hatred."
Mr Sarwar has revealed how Glasgow's ethnic minority communities have been alerted to allegations of five serious hate crimes in the past 10 days.
These are said to include an allegation that a schoolboy asked a young girl if he could pull her hijab off and film it to earn "points" for the campaign - which assigns these for crimes against Muslims.
Other alleged incidents in Glasgow include a woman allegedly being punched in the face outside a supermarket, and another woman allegedly racially abused by three men and assaulted on a train.
Following the meeting, Mr Sarwar said: "We recognise the fear and alarm that the 'punish a Muslim' campaign is causing, which has no place in society. An attack on one person living in Scotland, regardless of faith, is an attack on us all.
"Our advice to people concerned by this campaign is to go about your daily life, but remain vigilant, and we urge everyone to look out for their friends, family and neighbours.
"Any suspicious or concerning activity should be reported to the police, and we have received assurances from Police Scotland there will be extra vigilance around faith buildings and where there are large gatherings."
Muhammad Adrees, convener of the Muslim Council of Scotland, said: "The letters are a chilling reminder of the very real danger and hatred facing ordinary Muslims every day.
"Although there are no known recipients in Scotland, they have nonetheless caused considerable alarm and the community needs reassurance, especially since the letters have already triggered Islamophobic incidents here."