McConnell's comments infuriated Democrats, who were quick to recall his move three years ago.
McConnell's decision proved fateful for Republicans, as Trump went on to defeat Democrat Hillary Clinton in 2016.
McConnell's campaign says Morgan's challenge will "end no differently" than anyone else who has challenged the senator.
During a March 2016 interview on Fox News, McConnell said Republicans were "following a long-standing tradition of not filling vacancies on the Supreme Court in the middle of a presidential election year".
Morgan was elected to the Kentucky House in 2016 but was defeated two years later. "If there is a vacancy next year, because the White House and the Senate are the same party, we would vote to fill the slot", McConnell's staff director wrote in an email to reporters listing previous statements. At the Paducah event, McConnell said confirming judges is the best way to have "a long-lasting positive impact on the country".
Supreme Court Justices Neil Gorsuch and Brett Kavanaugh attend the State of the Union address in the chamber of the House of Representatives at the Capitol Building in Washington, on February 5, 2019.
Late on Tuesday, Senate Democratic Leader Chuck Schumer, in response to McConnell's remarks, said on Twitter: "Senator McConnell is a hypocrite". The vacancy created by Scalia's death was filled by conservative Neil Gorsuch while swing vote Anthony Kennedy, who retired, was replaced by Justice Brett Kavanaugh after an acrimonious brawl previous year.
"McConnell added: "What can't be undone is a lifetime appointment to a young man or woman who believes in the quaint notion that the job of the judge is to follow the law". When Donald Trump took office, Trump nominated Neil Gorsuch to fill the Court vacancy and it was approved. I said, 'Look, the only way the tax bill is permanent depends on the next election, ' " McConnell said.
McConnell cited "The Biden Rule", quoting then-Senate Judiciary Committee chairman Joe Biden's words in 1992 that President George H.W. Bush should not name a Supreme Court nominee until after the election that year, should a vacancy arise. Justice Ruth Bader Ginsburg, 86, has suffered a number of health issues in recent years, including cancerous growths in her lung and broken ribs. But much has changed since then, and many saw Biden's comments as naive, especially since he made no mention of McConnell's role in keeping Garland off the court. So that's the most important thing that we've done in the country, ' he said. "Seriously it's no surprise".
There had not been a situation since 1895 when a Democratic president made an appointment while Republicans controlled the Senate, making it hard to test the proposition.