The Swedish pilots union Svensk Pilotforening (SPF) also on Wednesday said its members intended to strike on August 10.
The union said Ryanair "had consistently refused to meet with and negotiate with representatives of SPF", accusing the Irish airline of wanting to choose its own negotiating team from the union.
The SPF said around 40 pilots at Skavsta airport, 100 kilometres (62 miles) southwest of Stockholm, would go on strike. Pilot unions in Belgium called on their members to join in industrial action on August 10.
Dutch and German pilots have also voted to strike unless they reach a deal with management.
"Ryanair needs a wake-up call and a strike in the Netherlands might be the only solution," the Dutch Airline Pilots Association said in a statement. The union said that Dutch law should be applied to Ryanair contracts and there should be "no more bogus self-employment and a sufficient sick pay and pension".
The German union Vereinigung Cockpit gave Ryanair until August 6 to submit a proposal for negotiation, noting that talks last Friday had broken down with no agreement.
"Since the start of our negotiations in January, Ryanair has been playing for time and even if Ryanair is not taking this ballot seriously, industrial action like in other European countries seems unavoidable in Germany as well," the union said.
Ryanair said it remained open to further talks with pilot representatives to discuss union recognition and collective labour agreements.
"In the interim, we have requested these pilot unions to give us seven days' notice of any planned strike action so that we can minimise the disruption to our customers by cancelling flights in advance and offering them alternative flights or refunds," a company statement said.
Ryanair, which flies in 37 countries and carried 130 million passengers last year, averted widespread strikes before Christmas by agreeing to recognise trade unions for the first time in its 32-year history.
But it has since struggled to reach agreement on terms with several of them.
The airline was hit by a round of strikes last week affecting 600 flights in Belgium, Ireland, Italy, Portugal and Spain.
It said the 100,000 affected passengers had all been put on alternative flights or would receive refunds.
Unions want the airline to give contractors the same work conditions as staff employees.
They are also seeking that Ryanair staff be employed according to the national legislation of the country they work in, rather than that of Ireland as is currently the case, which blocks the workers' access to state benefits. The Irish pilots' strike is focused on working arrangements, including annual leave and promotions.
Ryanair argues that since its planes fly under the Irish flag and most of its employees work onboard planes, its staff are covered by Irish law. Ryanair is Europe's biggest budget airline by passenger numbers, and the second biggest overall behind Germany's Lufthansa.
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