State labour mediator Juhani Salonius said the two sides remained too far apart for him to offer another compromise proposal. The Paperworkers' Union rejected his first proposal earlier this month.
Salonius said talks might resume next week, before the Midsummer holidays.
This week, the union said it was ready to make concessions in a central row over operating paper mills through public holidays.
Meanwhile, several other trade unions have launched measures against the Finnish Forest Industries Federation to support the Paperworkers' Union.
Plants producing cardboard and packaging materials, which had re-opened earlier in June, will now close again.
Finland's paper mills have been at a standstill for a month.
Paper Stocks Running Low The lengthy dispute has emptied paper stocks. Finland has to rely mainly on imports of, for example, newspaper and toilet paper. A strange situation for a country that is more used to exporting those products.
Finnish publishers have had difficulties in finding enough paper for newspapers. As a consequence, subscribers are reading slimmer editions. Most of the news is now printed on paper from Russia. Magazines are hauling paper in from around Europe.
If the dispute drags on, the Finnish paper industry runs the risk of permanently losing customers to foreign rivals.
By the end of June, the dispute is expected to shave off one percentage point off the national growth rate. The lockout also hits local authorities in the form of lost taxes. Meanwhile many haulage firms face bankruptcy and lumberjacks are out of work.