At issue is Uruguay's insistence on keeping the pulp mill running and Argentina's claim it is polluting the Uruguay River that defines the border and surrounding area that overlaps Argentina.
Buenos Aires has already lost a legal battle over the pulp mill at the World Court, The Hague, Netherlands, but has vowed to fight on.
Argentine-inspired pickets blocked bridges leading from Argentina to Uruguay, provoking a defiant response from Uruguay. Mujica has said he will talk to Argentine officials to try and reach a deal but not because he would bow to pressure from the protesters.
Mujica ruled out any negotiations with the protesters' representatives although media reports said he had met with and talked to some of them.
Mujica has also conferred with Argentine President Cristina Fernandez de Kirchner and Argentine Entre Rios province governor Sergio Urribarri. So far, most of the optimistic comments about an imminent resolution of the dispute have come from the Uruguayan side.
The Argentine argument that the pulp mill is a source of pollution has been rebutted at international forums, including the International Finance Corporation, but strong environmentalist lobbies within Argentina have kept the issue alive. The Rain Forests Movement has also expressed reservations about the project.
At issue is the viability of the whole campaign against the pulp plant, built by Finnish firm Botnia, because there is no evidence the plant will pollute the river. Botnia says the plant uses the latest technology to turn eucalyptus into pulp, which is then exported to Asia and Europe. Environmentalists insist the long-term effects of the plant will still be harmful.
Protests are camped outside the outskirts of Gualeguaychu, the border town in Argentina's Entre Rios province, which has seen most of the protest action since the 1990s.
Analysts said the blockade of bridges was hurting both sides and causing distress to families that are divided across the bridges in the two countries. Uruguay's tourism sector has suffered as a result of the dispute.
Argentina decided to take the dispute to The Hague, arguing Uruguay contravened a bilateral treaty by not obtaining Argentine authorization for the plant. Uruguay counters that the treaty only requires the neighbors to inform each other of their plans, but not seek permission before undertaking any construction projects.
Mujica said his meeting with Urribarri opened the way for further dialogue which he was determined to pursue.
Mujica's predecessor, outgoing President Tabare Vazquez, refused point blank to talks with Argentina on the issue as long as the blockades continued. The pickets and blockades have continued on and off since 2006.