Their conference Wednesday follows an April 20 World Court ruling in The Hague, Netherlands, that talked down Argentina's sustained campaign to have the eucalyptus crunching plant relocated from the border river to Uruguay's hinterland.
The ruling also rejected Argentine claims the Finnish pulp facility harmed the environment, pointing out lack of scientific evidence but upbraided Uruguay for failing to consult with Buenos Aires before building the factory.
By all counts, that should have been the end of the matter, except for the presence on a border bridge of hundreds of Argentine protesters against the mill's polluting potential. The picketing began when the plant opened in 2006 and has gone on since, attracted environmentalist groups and burgeoned into a campaign that demands nothing less than the closure of the plant.
The campaign originally was fanned by Fernandez and was the prime mover behind the government's anti-Uruguay rhetoric. But, as it emerged after the World Court judgment, the protest is a multi-faceted political platform with a life of its own, independent of the Fernandez government.
After the court ruling, Fernandez aides tried to persuade the protesters to go home and reopen the bridge, without success.
Mujica, a former guerrilla fighter himself, hoped the court ruling would end the friction and start a new phase of friendship with Argentina. This is the Argentines' wish as well but can only be fulfilled once the pickets leave.
The stalemate gives Mujica an unexpected edge over the Kirchners, the president and her spouse and former president Nestor Kirchner, who wants to head the Union of South American Nations when it meets Monday to choose its leader.
Failure to reach a happy compromise with Uruguay could mean Kirchner being opposed as UNASUR chairman, analysts said.
Uruguay hopes the reopening of the bridge will provide its economy with new markets for goods and services in Argentina and other neighboring countries.
The pulp mill, although widely criticized by environmentalist groups, is seen as critical to Uruguay's plan for resource development and diversification amid fears climate change is set to affect the country's agriculture and water resources.
The rise in eucalyptus plantations in the country, however, has led to protests because the plant, used for pulpwood production, consumes large quantities of water.
Environmentalist groups have called eucalyptus growth in Uruguay indiscriminate with dire consequences for Uruguay's agriculture and soil quality. The ongoing pulp mill dispute with Argentina has meant that Uruguayan officials aren't too keen on highlighting environmental politics that may damage their case against Buenos Aires.