Washington (CNN) White House press secretary Sarah Sanders refused again on Tuesday to correct her August statement that President Donald Trump wasn't involved in drafting a misleading statement about his son's meeting with a Russian lawyer at Trump Tower.

"I'm not going to go into detail and go into a back-and-forth. I know that you guys would love to engage on matters of conversations between the special counsel and the outside counsel, but we purposefully" remain separate from special counsel matters, Sanders said when pressed by CNN's Pamela Brown.

A day earlier, Sanders referred questions on the matter to the President's outside counsel. The President's lawyer did respond, saying Trump did dictate the statement. Rudy Giuliani later said it was a mistake to say he didn't.

"It was a mistake," Giuliani, a lawyer for Trump in the Russia investigation, said on CNN's "Cuomo Prime Time" Monday . "I swear to God, it was a mistake."

But Sanders insisted she remain "walled off" from the outside counsel's work.

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