Tens of thousands of nurses and midwives have gone on strike in Ireland for better pay and conditions but the government has rebuffed their demands, saying it needs to save funds for a possible no-deal Brexit.

More than 35,000 walked out on Wednesday morning and in near-freezing temperatures mounted pickets at clinics and hospitals, causing the cancellation of services for about 25,000 patients.

The 24-hour strike by the Irish Nurses and Midwives Organisation (INMO) is the first of six days of industrial action planned for the next two weeks.

The union called its first national strike in two decades after talks with the government and the Health Service Executive, a state agency, broke down.

The INMO says nurses and midwives work longer hours and are paid less money than in 2008, when the global financial crisis prompted austerity measures.

“No nurse or midwife wants to go on strike, but we have been forced into this position by a government that just isn’t listening,” said Tony Fitzpatrick, its industrial relations director.

The government says nurses are to receive significant pay rises under an existing public service agreement and that the additional rise they are striking for would cost about €300m (£260m) a year, blowing a hole in the budget and triggering demands for hefty rises from other public sector workers.

The prime minister, Leo Varadkar, told the Dáil on Tuesday that fiscal responsibility was all the more urgent because of the increased probability of the UK crash out of the EU without a deal on 29 March.

“I have to be a taoiseach for the whole country,” he said. “We will have to find a lot of money to save people’s jobs.”

Earlier on Tuesday, the Department of Finance said a no-deal Brexit would slash growth in Ireland and cost potential 55,000 jobs by 2023.

Varadkar rejected opposition accusations that he was using Brexit as a stick to beat nurses and midwives. “This isn’t made up – and it’s not about blaming anyone,” he said. The only one to blame for Brexit was Britain, he said.

The state’s health budget – and credibility – is already reeling from the cost of a new national children’s hospital in Dublin, which is scheduled to open in 2022. Budgeted in 2016 at €983m, the cost has ballooned to €1.4bn and may exceed €1.7bn.