Assange appeared by videolink from prison as lawyers discussed the management of his hearing next week to decide whether he should be extradited to the United States.
A CIA spokeswoman declined to comment.
The request was reportedly made last Thursday, but only became known to the public on Monday.
Assange is being held in the high-security Belmarsh prison "as if he were convicted for a serious criminal offense."
"Julian Assange, 47, has today, Thursday 11 April, been arrested by officers from the Metropolitan Police Service (MPS) at the Embassy of Ecuador," police said.
In a statement, Ecuador's foreign ministry denied it had reached an agreement with the British government to jail Assange if he left the embassy.
That investigation was later dropped, but Assange fears he could be extradited to face charges in the United States, where federal prosecutors are investigating WikiLeaks.
President Lenin Moreno of Ecuador told radio stations on Tuesday that Assange has "repeatedly violated" the terms of his asylum.
In an email, Stone said the evidence was "innocuous Twitter direct messages" that have already been disclosed to the House Intelligence Committee and "prove absolutely nothing."
The lawsuit also names Trump's son Donald Jr., his son-in-law Jared Kushner and former associate Roger Stone as being part of the scheme to sway the election in his favor.