The Labour Minister also said his party and Fine Gael were in agreement that changes to the tax code were needed to give workers more take-home pay.
His comments came as Transport Minister Paschal Donohoe also said that the combined high rate of tax on ordinary workers should be addressed.
There have been a string of ministers calling for tax changes for incomes ahead of budget negotiations getting under way between both parties.
Mr Nash said the Government would shortly set up a low-pay commission which would look at the minimum wage and levels of low pay across the economy.
But successful employers should consider small pay increases for their workers, he said: “When firms become more productive, inevitably, workers will seek pay increases. That is happening and will continue to happen over the next period of time.
“Nobody is talking about trying to impose pay increases on firms that they couldn’t possibly afford that at this stage,” he said.
“If we did see increases, even modest increases in pay packets right across the various sectors in the economy, then I think we would see even greater improvements in the country’s economic position.”
Every firm would benefit from the personal taxation code being reviewed, he said.
“There is a requirement on successful employers to work with their staff, to move towards a situation where they can get to a space where they are talking about pay increases for productivity gains.”
The Louth TD said it was possible for the Government to look at and encourage both those changes.
But there was also a responsibility on employers to restore wage levels and this had already started in a modest way in recent years.
Mr Donohoe said that any measures or changes introduced in October’s budget would need to affordable. But he also said he favoured a tax cut for workers.
“I’m very much aware that for many people, if they agree to do an extra hour of work, for the €10 they will earn due to do that — if that’s what they’re paid — they’ll take home just over €5 of that, and that’s something that as the economy recovers, that we have to address.”
Meanwhile, Mr Donohoe also cautioned against further planned strike action by Irish Rail workers in September, which will coincide with hurling and football finals in Croke Park, Dublin.
He claimed that Irish Rail workers would lose more in wages for the days they go on strike than they would if they accepted proposed pay cuts. He said that the cumulative effect in lost revenue from this week’s two-day action had amounted to €1.5m for Irish Rail.