Löfven is meeting Germany's Vice-Chancellor Sigmar Gabriel, the French Prime Minister Manuel Valls and the President of the European Parliament, Martin Schulz.
News agency TT reports that Löfven, Faymann, and Gabriel, along with the Swedish Trade Union Confederation and its German and Austrian counterparts, put the finishing touches on a plan to push for an EU treaty amendment to strengthen the rights of wage-earners.
According to the Swedish government's website, they are discussing "work to ensure decent conditions in the European labour market."
The Social Democrats and the trade unions want to see more of a balance between freedom and rights, and believe that market economies, growth and the free movement of people, capital, and goods and services, most be combined with strong social rights.
"There's a twisted competition in which one has to compete with wages and worse conditions," Löfven, who used to be head of the IF Metall union in Sweden, told news agency TT, taking the example of the hauling industry. He said the dumped prices make it impossible for Swedish hauling companies to compete and called the situation unacceptable.