Union Chair Petri Vanhala says employees made redundant need more time to look for new work or further education.
He called on the government to implement an industrial help programme and for UPM to demonstrate its responsibilities to the community.
The union board will meet next Tuesday to discuss measures to assist those losing their jobs at the Myllykoski and Pietarsaari mills. Strike action has not been ruled out.
Forest industry giant UPM-Kymmene announced earlier this week it plans to lay off 1,200 workers across Europe, including hundreds in Finland. The company aims to reduce magazine paper production capacity by 1.3 million tonnes per year in Europe.
UPM's Myllykoski mill in Kouvola, eastern Finland, is slated for closure by the end of the year, and other cuts will be spread across Germany and France. Cutbacks also target UPM's units in Lahti and Pietarsaari.
In all, up to 650 workers in Finland now face redundancy, 375 of them at the Myllykoski mill, which was founded in 1892.