Police in Wales are stepping up patrols near mosques after the attacks which killed 49 people in Christchurch.
A vigil was be held in Cardiff on Friday night to honour the victims of the mosque shootings in New Zealand.
First Minister Mark Drakeford said Wales stood with New Zealand in its "resistance to the forces of darkness".
The Muslim Council of Wales called on the Welsh Government to develop a "specific strategy for countering far-right extremism".
Speaking at the vigil, which took place at the Temple of Peace in Cathays Park, Mr Drakeford said the gathering showed the level of "strength and solidarity" in Wales towards those affected by the "awful events" in New Zealand.
He added: "It is also a message to communities here in Wales, who are fearful that what they have seen elsewhere may give license to people in this part of the world."
Wales rugby captain Alun Wyn Jones, said: "On behalf of the Welsh Rugby Union players and staff we pass our respects to everyone affected with events that have gone on in New Zealand.
"Obviously there's close links with a lot of our staff and a few players so we would like to extend that."
The Muslim Council of Wales said it was "shocked and hurt" by the shootings in "such an idyllic and quiet place". It called them a reminder that "hatred can appear any place and at any time".
The council said religious hate crime had "rocketed by 40% across England and Wales in just one year, with more than half targeted at Muslims".
In Wales, the council added there had also been a "resurgence in the activity and organising of far-right groups".
It called on public bodies to adopt the All Party Parliamentary Group definition of Islamophobia "as steps towards preventing future tragedies such as this from taking place".
South Wales Police said that in common with other UK forces, it would carry out extra patrols on Friday and over the weekend.
South Wales Police Chief Constable Matt Jukes tweeted that such tragedies sent "shockwaves across faith communities", and his force would provide a "visible presence at our mosques".
Dyfed-Powys Police also said it would step up "reassurance patrols" around mosques and increase contacts with communities of all faiths.
Gwent Police and Crime Commissioner Jeff Cuthbert said: "Today we must stand together in solidarity to remember all those who lost their lives in this hateful, abhorrent terrorist attack.
"We all have a responsibility to teach people that hate abuse is wrong from a young age and stand up against vicious extremism in all its forms."
PC Robert Newton-Miller, of North Wales Police, said the force was placing officers at mosques, and had been in touch with imams.
"I will be attending Friday prayers today to deliver a message to the communities in North Wales in order to promote our support and reassurance during these difficult times," said PC Newton-Miller.
The Church in Wales said: "In the face of this kind of hatred, it is more important than ever that we reach out in friendship and solidarity to our neighbours. We pray that God will be close to those most deeply affected, and give courage to all those who may now be fearful of showing their faith.
The Bishop of St Davids, Joanna Penberthy, added: "All of us together must condemn violence and stand against hatred and prejudice."