The victor will serve the last two years of the six-year term vacated when Republican Thad Cochran retired for health reasons.
During a speaking engagement in Jackson on Monday, Hyde-Smith repeatedly refused to answer reporters' questions about the comment, according to ABC News' affiliate WAPT.
The comments came at a press conference announcing the endorsement of a pro-life group for Hyde-Smith's reelection bid.
At a campaign event earlier this month, Mississippi Sen.
MS was the most bloodthirsty state in the Union when it came to lynching Blacks with 581 recorded between 1882 and 1968, according to the NAACP.
His latest response comes a day after Espy condemned her remark in a statement: "Cindy Hyde-Smith's comments are reprehensible".
"Now, in a political campaign, people can make anything you say what they want it to say".
"We need leaders, not dividers, and her words show that she lacks the understanding and judgment to represent the people of our state", he said in a statement to The Washington Post.
Hyde-Smith was appointed to the post by Mississippi Governor Phil Bryant after former-U.S. Sen. She will serve until the special election is resolved. The victor gets the final two years of Cochran's term.
A newly published video shows Sen. White obtained the recording the night before from an unidentified individual he described as "a very reliable, trusted source", he told the outlet.
"They are hurtful to millions of Mississippians who are people of goodwill", he said.
Trump has been vocal in his support for Hyde-Smith, tweeting in August that she is "strong" on issues such as job creation and his proposed southern border wall, helping him to "put America First!"
Derrick Johnson, president of the NAACP, said Hyde-Smith's comments, "prove once again how Trump has created a social and political climate that normalizes hateful and racist rhetoric".
But Hyde-Smith said her remark was just an "exaggerated expression of regard". "Hyde-Smith's decision to joke about 'hanging, ' in a state known for its violent and terroristic history toward African Americans, is sick".
In a state that even the legendary White reporter Peter Jennings once called "the most evil state in the country" - and is most notorious for hanging hundreds of Black men during the Jim Crow era of legal racial segregation - Cindy Hyde-Smith felt comfortable enough to say publicly and on video that she would watch someone being murdered through lynching.
GOP candidates have made numerous questionable race-related comments in the last few weeks.