It comes after the engineering firm announced 760 redundancies would be made across its four Northern Ireland facilities - Larne, Belfast, Springvale and Monkstown.
Finance Minister Sammy Wilson, who is an MP for the area, and local MLAs attended the meeting which sparked suggestions on how to replace the lost jobs.
These ideas will now be taken forward by a local task force.
The DUP minister said they had "a very good discussion."
"There are a number of things, immediate things, for those who have been made redundant or will be made redundant."
He said the council wanted to work with the Department for Employment and Learning (DEL) to make available some of their premises and expertise to host job fairs and bring employers to the area.
"We have looked at what might be done to try and replace the jobs that are being lost and some of the suggestions are that if there are jobs in the pipeline, or if Invest NI are talking to firms at present about increasing employment, or bringing employment to Northern Ireland then there are sites available here."
Town Mayor Geraldine Mulvenna told UTV a strategy is needed to help those who have lost their jobs, but she admitted it will be a difficult time for the area.
The Alliance Councillor said: "Larne Borough Council has been trying so hard in the past years to really try and turn the town around by bringing in more business and the community support is amazing.
"But I think it's going to have a very difficult, depressing impact on everyone, both businesses and in the community."
FG Wilson is moving production of its 400 series generator sets to Tianjin, China, to build the product closer to its growing customer base.
The announcement of the job losses was made by owners Caterpillar Inc. on Thursday, and comes after a further 160 cuts were announced earlier this year.
A statement said: "As a result of the evaluation of the small generator set business, announced in June, and adjusting production levels to better align with demand, Caterpillar is releasing up to approximately 760 people - a combination of salaried and production employees, as well as agency workers.
"To date approximately 170 agency workers included in that total have been released."
Robert Kennedy, Northern Ireland Operations Director, said: "We value our employees' contributions, and these actions are not a reflection of them, but rather of the business climate."
The news has been met with shock and disappointment.
Enterprise Minister Arlene Foster called it "a major blow to the Northern Ireland economy."
Following a crisis meeting at Stormont, First Minister Peter Robinson said: "It's a massive blow for local communities and particularly for the families that are involved.
"We can put money out there to boost business and to create jobs but if you've had a steady income for a long period of time in a job that suits the skills that you have, even the disruption of moving to another job, even if they were immediately available, is very significant."
Unions have reacted angrily.
Jimmy Kelly of UNITE said: "When we meet the workforce on Monday, we will be outlining what we have been told by the management and we will be taking guidelines from our members to what the next steps are because one thing we are not going to do is co-operate with a plan which is the start to dismantling the whole plant.
"Certainly, as for how we go forward from here, I don't see in the current climate that it will be easy to have jobs available."
Meanwhile Ian Coulter, Chairman of CBI, said he believes work can be found for those engineers who were made redundant.
He said: "Engineering in Northern Ireland should be a strength of ours, with the number of particularly indigenous engineering companies that are in growth and very ambitious.
"I know next week, just by coincidence there was a meeting that was pre-arranged, Steven Farry, Invest NI are meeting a number of CBI members in the manufacturing and power services sector to talk about skills and to talk about potential shortages.
"So if there is a solution there can we look at how we can transplant these people, potentially maybe re-skill them and get them into another job."