The Unite trade union is calling for the minimum wage to be increased by one euro.
The group is are calling for a Wage Recovery Package to be implemented to increase incomes for those low rates of pay.
The union also says that the country is in a low-pay crisis, with a widening gap in wage levels.
As well as increasing the minimum wage to €9.65 an hour, the union is also calling for measures including "strengthening and extending JLCs (Joint Labour Committees)" and "introducing comprehensive labour rights legislation to bring us into line other EU members."
Irish Secretary of Unite Jimmy Kelly, says the Low Pay Commission should increase the minimum wage as soon as possible:
The Tánaiste and Labour Party leader Joan Burton said last month that the coalition will increase the minimum wage if the Low Pay Commission recommends it.
Speaking at the party's national conference, she said fair wages and decent working conditions are essential, workers are entitled to a living wage and an increase in the minimum wage could be on the cards.
The Low Pay Commission will be made up of nine members and will take a range of issues into consideration in making its recommendation. The members include trade union and business representatives, economy experts and a representative of the Migrants Rights Centre Ireland.
Dr Donal de Buitléir, director of PublicPolicy.ie, is serving as chairperson.
Issues to be considered include changes in earnings since the last increase in the National Minimum Wage in 2011, employment and unemployment rates, the cost of living and national competitiveness.
The commission will consult with appropriate interest groups and people who are on the minimum wage, as well as employers in sectors associated with low pay.
The group's first report is due to be published in July - and the Government will respond before the Budget.