"The war on whistleblowers must end," the 41-year-old Australian told reporters Sunday, speaking from a small balcony at the embassy.
"I ask President [Barack] Obama to do the right thing. The United States must renounce its witch-hunt against WikiLeaks. The United States must dissolve its FBI investigation. The United States must vow it will not seek to charge our staff or supporters," he said.
Assange also called on the U.S. to release army private Bradley Manning, charged with leaking classified information. The 24-year-old intelligence analyst is accused of aiding the enemy by causing hundreds of thousands of classified documents to be published on the WikiLeaks website.
"On Wednesday, Bradley Manning spent his 815th day of detention without trial. The legal maximum is 120 days," Assange said at the news conference.
Assange took refuge inside Ecuador's Embassy in London on June 19 to avoid extradition to Sweden over sexual misconduct allegations. The WikiLeaks founder sought shelter at the embassy after exhausting all routes of appeal in the U.K. to avoid being sent to Sweden.
British officials had said he would be arrested if he were to step foot outside the embassy.
Assange thanked Ecuador president Rafael Correa for granting him political asylum on Thursday.
Correa on Saturday continued to stand behind his decision to grant political asylum to Assange.
At a rally in the city of Loja, in the southern part of the country, Correa said Ecuador made the decision in a "responsible, calm and sovereign manner," in order to "protect the life and human rights of Mr. Julian Assange."