President Donald Trump's abrupt decision to terminate FBI Director James Comey Tuesday raises questions but shouldn't lead to the appointment of a special prosecutor to consider Russia's connections to the 2016 election, Sen. John Thune said Wednesday.

Democrats, including South Dakota Democratic Party leaders, have called for Congress to hire an independent prosecutor to take up the investigation.

In an interview with Fox News, Thune said Democrats' attempts to launch a new probe are aimed at generating public support and are unwarranted.

►Analysis:Donald Trump's decision to fire James Comey means the campaign won't end

"That's not going to happen," he said. "There's plenty of investigations out there already into this matter, which are independent and objective."

Thune and Rep. Kristi Noem said they'd like additional explanation from Trump on his decision to fire Comey.

“While this was ultimately a judgement call by the president, I think there are questions about timing that the administration and Justice Department are going to need to answer in the days ahead," Thune said in a statement.

Sen. Mike Rounds said the announcement of Comey's termination was unexpected, but investigation into Russian ties wouldn't be hindered by the firing.

“I was surprised at the timing of Mr. Comey’s termination,” Rounds said in a statement. “However, we expect the investigations into Russia’s attempt to interfere with the 2016 election to continue. His termination will not be allowed to impede in these investigations.”

Trump in a letter to Comey said the FBI needs leadership that "restores public trust and confidence" in the organization.

►More:Comey's dismissal had nothing to do with Russia probe, Trump says

The president defended the decision in a series of tweets Wednesday morning, saying, "Comey lost the confidence of almost everyone in Washington, Republican and Democrat alike. When things calm down, they will be thanking me!"

Leaders of the South Dakota Democratic Party on Tuesday called on the state's Republican delegates to request a special prosecutor in the case.

"There can be no doubt now that an independent commission - with subpoena power - is the only way to ensure a full and fair investigation into these matters," Ann Tornberg, South Dakota Democratic Party Chair, said in a statement.

Follow Dana Ferguson on Twitter @bydanaferguson, call 605-370-2493 or email dferguson@argusleader.com