"We have to increase the pressure massively," Verdi deputy leader Andrea Kocsis told journalists in Berlin.
Verdi says that the Post has not made any concessions towards solving the conflict through six rounds of talks over pay and working hours for 140,000 employees.
At the heart of the argument is the company's plan to create regional subsidiaries where former postmen will be employed at the lower wages typical of logistics companies.
The union is fighting for the right to continue representing those employees in collective bargaining with the Post.
At the same time, it has been pushing for a one-off €500 payment to every worker in 2015 and a pay rise of 2.7 percent next year.
But Deutsche Post refused, saying that it would cost €300 million to meet Verdi's demands - "a tangible worsening of our existing competitive disadvantage," human resources chief Melanie Kreis said.
Kreis argued on Monday that the Post already pays double the wages of its competitors.