CNN aired video of the raid at Stone's home in Fort Lauderdale, Florida, showing agents in body armor using large weapons and night-vision equipment, running up to the home and banging on the door.
He said he will plead "not guilty" to the charges. It alleges that Stone informed unidentified senior Trump campaign officials of what Stone was hearing about plans by the anti-secrecy website WikiLeaks regarding the hacked emails.
"There's no circumstance under which I would bear false witness to the president".
The 24-page indictment brings the investigation even further into the president's circle of advisers and suggests that Trump campaign officials were eager to exploit the stolen messages for political gain.
Roger Stone is the sixth Trump associate charged by Mueller.
Graphic shows people indicted in connection with the special counsel probe into Russian meddling in USA elections.
As a campaign advisor, then, Stone could have colluded - and Giuliani wouldn't deny it.
In a tweet Friday, Podesta turned Stone's words against him, writing that it was now "Roger's time in the barrel".
It notes that Stone then continued to pass information along about WikiLeaks and quotes conversations he had with Steve Bannon, who served at the highest level of the campaign and later joined the White House.
In Saturday's response to the indictment, which is part of Mueller's investigation into potential collusion between the Trump campaign and Russia, Trump attempted to put the focus on several figures he has said need to be investigated.
Stone had also blasted the prosecution in a circus-like atmosphere outside the courthouse on Friday, as supporters cheered him on and jeering spectators shouted "Lock him up".
The Kremlin has denied interfering in the election.
The indictment referred to an October 2016 email from a "high-ranking Trump Campaign official" asking Stone to inquire about future releases of emails by "Organization 1".
Stephanopolous asked Stone what he hopes to gain by doing interviews after being indicted.
It adds to the growing list of Trump associates who have been charged in the special counsel's probe.
Credico and Stone would go on to have discussions about ongoing investigations. Those indicted include 12 Russian military officers and 13 Russian nationals accused of leading a campaign to interfere in the USA election.
Those people include former close associates of Trump such as his one-time lawyer Michael Cohen and former campaign chairman Paul Manafort as well as 12 Russian intelligence officers.
Stone's reputation as an aggressive political operative dates back to the Watergate scandal of the 1970s when he was working for Nixon.
The Trump campaign apparently did communicate with Stone - a well-known friend to the campaign and to the candidate himself.
He reportedly does not wear socks, and favours custom-made suits.
"Mr. Stone, during his time as a student at George Washington University, was a junior scheduler on the Nixon reelection committee. Mr".
He also embraced deeply a key lesson from the 1972 campaign: that Republicans had to appeal to a base of white, middle class suburban and rural voters.
Stone had predicted his own arrest for months, trying to raise money for his defence online while making sure to stay in Trump's good graces, perhaps with an eye on a presidential pardon down the road.