According to the BBC, the letter criticises Sweden's prosecutor for a "serious failure" to complete an investigation into rape allegations dating back to 2010. Ecuadorian authorities accuse the prosecutor of a "lack of iniative".
Julian Assange has been confined at the Ecuadorean embassy in London, where he has asylum, for nearly five years. British police say he will be arrested if he leaves the embassy.
The Australian has always protested his innocence, but refused to go to Sweden for questioning fearing he would be extradited to the United States for publishing classified documents online.
In November last year, Assange was finally interviewed at the Ecuadorian embassy, six years after the accusations made against him during a short stay in Sweden.
The interview was conducted by an Ecuadorian prosecutor who put forward questions from the Swedish prosecutors. His answers were submitted as a written statement to Swedish prosecutors.
Earlier this month, Assange's lawyer, Per Samuelson, called for Sweden to drop its investigation into his client.
It followed US Attorney General Jess Sessions' comments that arresting Assange was "a priority" for the United States after Wikileaks published emails hacked from the Democratic National Committee during last year's election campaign.