Sen. Lamar Alexander, R-Tenn., a key impeachment swing vote, announced Thursday that he will not join Democrats in voting to call witnesses in President Donald Trump's Senate impeachment trial, suggesting that there may not be enough GOP votes for the trial to advance to that next stage.

"I worked with other senators to make sure that we have the right to ask for more documents and witnesses, but there is no need for more evidence to prove something that has already been proven and that does not meet the U.S. Constitution's high bar for an impeachable offense," he said on Twitter.

Alexander, who's retiring from Congress at the end of the year, was among a small group of Republican senators who had hinted during the trial that they could vote to hear from witnesses who had firsthand knowledge of Trump's conduct toward Ukraine.

In a lengthy statement, Alexander also said Trump's conduct on his July 25 call with the Ukrainian president was "inappropriate," but he suggested that it was not an impeachable offense.

"It was inappropriate for the president to ask a foreign leader to investigate his political opponent and to withhold United States aid to encourage that investigation," Alexander said.

"When elected officials inappropriately interfere with such investigations, it undermines the principle of equal justice under the law. But the Constitution does not give the Senate the power to remove the president from office and ban him from this year's ballot simply for actions that are inappropriate."

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Alexander also appeared to adopt the argument made by the president's defense team during the trial, calling the inquiry a "partisan impeachment."

"Even if the House charges were true, they do not meet the Constitution's 'treason, bribery, or other high crimes and misdemeanors' standard for an impeachable offense," he added, saying voters should decide at the ballot box.

During the trial, the president's defense argued that the articles of impeachment are not valid because the standard for impeachment requires a crime and Trump was acting within his powers as the head of the executive branch. However, House managers rejected that argument, calling it an "a remarkable lowering of the bar" and saying it would give a president broad powers to do whatever he or she wanted.

Sen. Susan Collins of Maine, another Republican whom Democrats were eyeing for support, said late Thursday that she would support calling witnesses, however.

"I believe hearing from certain witnesses would give each side the opportunity to more fully and fairly make their case, resolve any ambiguities, and provide additional clarity. Therefore, I will vote in support of the motion to allow witnesses and documents to be subpoenaed," she said in a statement after the second day of senators' questions wrapped up.

Four Republicans would have to vote alongside all Democrats for new witness testimony to be admitted. Republican Sens. Lisa Murkowski of Alaska and Mitt Romney of Utah were also considered to be top targets for Democrats who want to hear new witness testimony and documentary evidence at the Senate trial. Romney will vote for witnesses on Friday, two aides told NBC News.

Alexander privately huddled with Murkowski during Thursday's dinner break, according to a senior Republican aide close to Alexander. The two lawmakers discussed where they are on witnesses but were not coordinating their final decision, the aide told NBC News.

Murkowski said late Thursday that she had not made a decision. After Thursday's session adjourned, she told reporters: "I am going to go reflect on what I have heard, re-read my notes and decide whether I need to hear more."

Former national security adviser John Bolton and acting White House chief of staff Mick Mulvaney are among the figures Democrats have called on to testify.

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Alexander, who served two terms as governor of Tennessee before two unsuccessful runs for president, has a history of bipartisanship. He worked with Senate Minority Leader Chuck Schumer, D-N.Y., and a handful of other Democrats to make it easier for the Senate to confirm presidential nominees.

As chairman of the Health, Education, Labor and Pensions Committee, Alexander worked closely with Sen. Patty Murray, D-Wash., the committee's ranking member, to advance sweeping education reforms.

Alexander asked his first question during the Senate trial Thursday, along with two other senators, in which he pressed the House managers to compare the bipartisanship of the impeachment proceedings against Trump and presidents Richard Nixon and Bill Clinton. Nixon resigned in 1974 before he could formally be impeached.

"Specifically how bipartisan was the vote in the House of Representatives to authorize and direct the House Committees to begin formal impeachment inquiries for each of the three presidents?" Alexander asked, signaling possible frustration that the House vote against Trump was not bipartisan.

Rep. Zoe Lofgren, D-Calif., who served on the House Judiciary Committee staff during the proceedings that could have led to Nixon's impeachment and was a member of the committee during the Clinton and Trump impeachments, said neither of the earlier processes was truly bipartisan.

"In the Nixon impeachment,we look back and we think about the vote on the House Judiciary Committee that ended up bipartisan, but it didn't start that way," she said. "When it came to the Clinton impeachment, that was, again — it started out along very partisan lines. And it ended along partisan lines."