"I think probably as a layman looking at this kind of thing we need to find someone who is very, very objective who can get to the bottom of these accusations," Kelly said in an interview on Fox News.
A special counsel would be appointed by the Justice Department.
Republicans in Congress last week launched an investigation into an Obama-era deal in which a Russian company bought a Canadian firm that owned some 20 percent of US uranium supplies.
Some Republicans have said Hillary Clinton's State Department approved the deal after her husband's charitable foundation received a $145 million donation. The New York Times has reported that Clinton, a Democrat who lost to Republican Trump in the 2016 election, did not participate in the decision.
Republicans have also raised questions about whether Democrats funded a dossier put together during last year's presidential campaign that detailed accusations about Trump's ties to Russia.
Kelly's call for a special counsel to investigate Democrats comes as a probe by special counsel Robert Mueller into possible collusion between the Trump campaign and Russians produced its first charges and a guilty plea.
A grand jury impaneled by Mueller indicted former Trump campaign manager Paul Manafort and aide Rick Gates on Monday. A third former Trump adviser, George Papadopoulos, pleaded guilty in early October to lying to the FBI, it was announced on Monday.
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