“We are trying to ensure that the Swedish justice system recognizes the resolution and its binding nature,” Baltasar Garzon, who leads Assange’s legal team, told reporters in Quito.
Assange, 44, recently marked the start of his fifth year inside Ecuador’s UK mission in a bid to avoid extradition.
The anti-secrecy campaigner is wanted for questioning over a 2010 rape allegation in Sweden.
He fears that from Sweden he could be extradited to the United States over WikiLeaks’ release of 500,000 secret military files.
The UN Working Group on Arbitrary Detention issued a legal opinion in February saying Assange’s confinement in the Ecuadoran embassy amounted to arbitrary detention by Sweden and Britain.
It said Assange should be able to claim compensation from the two countries.
“It has not happened, it’s predictable,” Garzon said.
Both Britain and Sweden have angrily disputed the UN group’s findings.
A Stockholm district court last month maintained a European arrest warrant against Assange, rejecting his lawyers’ request to have it lifted.