Mook said the idea that Russia leaked Democrats' emails to possibly help Trump was "disturbing."
"We need to be concerned Trump and his allies made changes to the platform to make it more pro-Russian, and we saw him talking about how NATO shouldn't intervene [in Russian disputes]. So I think when you put it all together, it's a disturbing picture," he said.
In a statement emailed to The Washington Post, Trump's campaign called that assertion a "joke."
"This shows that Hillary Clinton will do and say anything to win the election and hold onto power in the rigged system," said Jason Miller, a senior communications adviser for Trump.
When Tapper pressed him further, Mook made a connection between the June breach of the DNC's network by Russian government hackers and WikiLeaks's publication on Friday of 20,000 emails from DNC officials.
Some of those emails appear to show party officials questioning Sanders's viability and discussing how to use his faith against him.
"If they are the ones that took them, we have to believe they are the ones releasing them," Mook said.
He doubled down on that assertion in an interview with ABC's George Stephanopoulos on Sunday.
However they got released, some of the emails could be damaging to the Democratic Party's attempts to unify at its convention in Philadelphia this week. The DNC is supposed to be neutral throughout the primary process, but Sanders spent much of it accusing the DNC and its chair, Rep. Debbie Wasserman Schultz (Fla.), of supporting Clinton behind the scenes.
Wasserman Schultz will not speak at the convention, CNN reported.
On Sunday, Sanders repeated his call for Wasserman Schultz to resign. Mook didn't go that far in his interviews on Sunday, instead saying, "I'm going to leave that to the DNC, because I don't have all the facts."