It follows the breakdown of talks between the two sides at the weekend and a strike earlier this week that shut 40 paper and 14 board mills.
The extension, if it goes the full course, will lead to Finnish mills being closed until 15 June, which one Swedish manufacturer said, "would create considerable problems with supply".
Finnish Forest Industries Federation communications manager Anne Kokkonen said the situation was bad.
Employers had decided that they could no longer tolerate the shutdowns, and had decided it was better to keep the mills closed, due to the risk of environmental damage or machines breaking. The lockouts are estimated to be costing 28m (e40m) per day for the mills.
"Negotiations will re-commence on 20 May, and we hope that a deal might happen quite soon," said Kokkonen.
A paper buyer at one UK publisher said stocks were fine for the original two-week lockout, but four weeks would reduce them to a bare minimum.
"This would have a knock-on effect for our deliveries scheduled for the end of May and beginning of June," said the buyer.
A source at a Finnish manufacturer in the UK said his company had foreseen the situation and built buffer stocks to sustain contractual business.
"I think the four weeks is a scare tactic," said the source.
The Swedish paper union Pappers is supporting Finnish workers with an overtime ban, with no plans for any further action.
Story by Andy Scott
Have your say in the Printweek Poll
Related stories
Latest comments
"Thank you for the opportunity to comment on this Jo, and PrintWeek!
Please feel free to get in touch with the Howden Print Team to arrange your own Free of Charge Cyber Micro-Penetration Test to help..."
"I never quite understand the statements such as "achieved such a positive outcome for this well-established business".
The established business unfortunately failed and no longer exists, a..."
"Genuinely sorry to read this."
Up next...

Certification can help
Printers urged to check exposure to cyber crime

Held at Aston Martin Racing Technology Campus
Xerox highlights power of data at client event

Support for important local event
Fujifilm contributes to Operation Dynamo commemorations

Standout addition to press hall