Moreno, who was sworn in earlier this month, has broken with his predecessor and mentor Rafael Correa, who had said Assange was a "journalist" and granted him asylum in London in 2012 to avoid extradition to Sweden over rape allegations.
Assange, who denies the allegations, feared Sweden would hand him over to the United States to face prosecution over WikiLeaks' publication of thousands of classified military and diplomatic documents in one of the largest information leaks in U.S. history.
During the campaign, Moreno had already taken a tougher stance on Assange, warning him "not to intervene in the politics" of countries friendly to Ecuador.
"Mr. Assange is a hacker. That's something we reject, and I personally reject," Moreno told journalists on Monday.
"But I respect the situation he is in, which calls for respect of his human rights, but we also ask that he respects the situation he is in."
Assange dodged an eviction order in Ecuador's April election, after the right-wing candidate who had vowed to kick him out of the embassy lost to Moreno.
Still, the tight presidential election highlighted just how vulnerable Assange is should a new government be ushered in.
In May, Swedish prosecutors dropped their investigation into the rape allegations but British police said Assange would still be arrested if he left the Ecuadorean embassy where he has been holed up for five years.
(Writing by Alexandra Ulmer; Editing by Sandra Maler)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)