The reports have prompted some electoral voters to call for an intelligence briefing on the extent of any Russian interference before the electoral college vote on Monday.
John Podesta, former chairman of Hillary Clinton's campaign, has publicly supported those electors' demands.
On Sunday, Conway dismissed such calls.
“The entire nonsense about the electors trying to use the Russian hacking issue to change the election results is really unfortunate,” she told Dickerson. “I think that actually undermines our democracy more than any other conversation that we’re having right now.”
Dickerson pressed Conway several times about whether Trump had evidence that Russians did not hack the election that would cause his stance to differ from that of the wider intelligence community.
“The president-elect receives intelligence briefings that I am not privy to,” Conway responded.
She also suggested that President Obama's recent tough talk on Russia came because he was “under political pressure” to do so. On Friday, Obama said the United States will retaliate against Russia “at a time and place of our own choosing” over its malicious cyber activities during the U.S. election.
Dickerson asked whether Trump supported Obama's approach, a question Conway did not directly address.
“The president-elect respects the ability of President Obama to do what he sees necessary in any number of different arenas,” Conway said. “It does seem to be a political response at this point, because it seems like the president is under pressure from Team Hillary, who can’t accept the election results.”
Trump has been criticized for his friendly posturing toward Russian President Vladimir Putin and has minimized the allegations that Russia interfered with the U.S. election.
Like Conway, Trump's surrogates have largely done the same, suggesting that reports from the intelligence community are an attempt to delegitimize Trump's win.
Trump and his transition team's stance on the issue is at odds with several members of the Republican Party.
Earlier this month, four high-ranking senators called for a thorough investigation of alleged Russian meddling in the election.
Senate Armed Services Committee Chairman John McCain (R-Ariz.) and Sen. Lindsey O. Graham (R-S.C.) joined incoming Senate Democratic leader Charles E. Schumer (N.Y.) and Armed Services ranking Democrat Jack Reed (R.I.) in issuing a bipartisan statement.
“This cannot become a partisan issue,” the statement read in part. “The stakes are too high for our country.”
In a separate appearance Sunday on CNN's “State of the Union,” McCain called for a select Senate committee to investigate Russia's cyber activities during the election.
McCain told host Jake Tapper that there was “no doubt” that Russia interfered — and that even if it would not have affected the outcome of the election, it was a serious matter.
“I have seen no evidence that the election would have been different, but that doesn’t change the fact that the Russians and others — the Chinese, to a lesser degree — have been able to interfere with our electoral process,” McCain said.
“If they are able to harm the electoral process, then they destroy democracy.”