An inter-religion council is to be set up
Mr Morgan's comments were made after a meeting of religious and political leaders in Wales.
Denouncing those who attacked the Muslim community as "brain dead", he said that a multi-faith council would be created to deal with the crisis.
The move follows reports of alleged incidents since the terrorist attacks on the World Trade Center on 11 September.
Muslim leaders have expressed concern at isolated incidents of vandalism and verbal abuse of Muslim women in south Wales.
Home Secretary David Blunkett announced new measures to clamp down on religious intolerance at the Labour Party's annual conference in Brighton.
Mr Morgan will discuss measures to ease tensions with the Race Equality Council and police.
Muslim business community leader Saleem Kidwai said the purpose of the talks was to "reassure people and comfort them".
"That is what we need at the moment," said Mr Kidwai.
"We are concerned about these isolated incidents and acts of vandalism."
Incident claims
Senior religious and ethnic leaders want police chiefs to keep them informed of developments.
South Wales Police have said that there has been an increase in the number racial attacks recorded since the attrocities.
Earlier this month, Muslim leaders in Swansea investigated a claim that a woman ripped a headscarf from a Muslim schoolgirl.
There were also claims that a mosque in the city had been stoned and death threats received.
This led to calls for restraint, amid concerns that Muslims could become targets for racial attacks.
Assembly Finance Minister Edwina Hart - who has met with Muslim community leaders - has added to the calls for restraint.
Wales has one of the oldest Muslim communities in the UK, centred in Cardiff Bay, with the oldest mosque dating back to 1860.
It is estimated that 50,000 Muslims live in Wales.
Islamic leaders in Wales have deplored any acts which may have been carried out in the name of Muslims.