British foreign secretary William Hague will meet with Ecuadorian foreign minister Ricardo Patino at the United Nations in New York to talk about Assange, who is about to mark his 100th day at the Ecuadorian embassy in London.
Assange has been offered political asylum by Ecuador, but faces arrest and extradition to Sweden, where he is wanted for questioning over alleged sex offences.
The 41-year-old fears that he will then be extradited to the United States to face questioning over Wikileaks.
"We hope [this] meeting will mark the beginning of a new chapter in seeking a solution to the present situation," an Ecuadorian official told Sky News.
"For the part of the Ecuadorian government, we are more than willing to find an amicable answer that respects the values of international human rights and the integrity of sovereign nations."
Assange has also made another appeal to the US via Russia Today, asking the country's government to "cease its persecution of Wikileaks, our people and our sources".