Protestors who gathered outside the council buildings accused the council of not doing enough to protect them.
Leader Charlie Gordon (Lab), Lord Provost Alex Mosson (Lab) and the council's spokesman on asylum seekers Archie Graham (Lab) met representatives for the asylum seekers to consider emergency measures to tackle rising violence.
The meeting came the day before another asylum seeker was stabbed.
the Sighthill area where many are housed and more money for police to tackle racist crime.
A council spokesman said: 'They say we haven't done enough to inform people about their problems. We are working with the police to improve the situation.'
The murder, which is being treated by police as a racist attack, comes as a blow to the council which recently organised a multi-cultural festival to try to reduce escalating animosity towards asylum seekers.
The Scottish Refugee Council said there had recently been 'a huge number of racist attacks'.
The government's dispersal scheme for asylum seekers has come under fire for not providing the necessary support away from London and the south east.
A spokesman for Welsh first secretary Rhodri Morgan said in Wales housing was allocated but no asylum seekers arrived and the vacant properties are now occupied.
Kent CC leader Sandy Bruce-Lockhart (Con) said the government's dispersal system is easing the situation.
He said: 'In the last four years we have seen the number of asylum seekers coming in to the county grow from 50 to 12,000 a year. The dispersal system is now bringing some help to counties like Kent.
'Greater effort is now being made to
deal with applications more quickly, but more asylum seekers are being granted extended leave to remain for four years. It is this slow and ineffective asylum appeal system which damages race relations.'