Speaking in the Dáil, Mr Cowen said it was not clear what it would achieve as it would be far better for the unions to continue in discussions with the Government on how to achieve savings in next month's budget.
Labour leader Eamon Gilmore said the Taoiseach's appeal was meaningless and he should engage directly with the unions rather than leaving it to his officials.
Mr Gilmore warned the Government that it was sleep-walking into a strike and leading the country down the road of conflict and industrial action.
Earlier, it emerged that SIPTU's public sector membership has voted in favour of industrial and strike action to oppose the Government's plans to cut pay and public spending.
This will significantly boost the numbers taking part in the public sector strike next Tuesday, 24 November.
Last week, teachers from the three main unions voted in favour of a one day strike, which will see the country's schools closed for the day.
90% of the union's health sector members voted for industrial action, with 85% being prepared to strike. In the third level education service, members backed both industrial action and strike action by 79%.
