Senate Republicans on Sunday acknowledged President Donald Trump was wrong to pressure Ukraine for his own political benefit, even as they defended their decision to prohibit new evidence in the impeachment trial while pressing ahead with the president's all-but-certain acquittal.

The remarks from key Republicans — including Sens. Lamar Alexander of Tennessee and Joni Ernst of Iowa — came after the Trump administration revealed the existence of e-mails that could shed light on the president's reasons for withholding military aid to Ukraine.

"I'm going to vote to acquit," Alexander said on NBC News' "Meet the Press." "I'm very concerned about any action that we could take that would establish a perpetual impeachment in the House of Representatives whenever the House was a different party than the president. That would immobilize the Senate."

One GOP senator, a close ally of Trump, suggested a sweeping Republican counterattack following Wednesday's vote to acquit the president.

"It's going to happen in the coming weeks," Senate Judiciary Committee Chairman Lindsey Graham said of the counteroffensive in an interview on Fox News.

Graham outlined a plan that would include an investigation of former Vice President Joe Biden, who is running for the 2020 Democratic presidential nomination, and a pursuit of the whistleblower whose account triggered the probe into Trump's efforts to pressure Ukraine.

It was unclear whether other Senate committee chairs were on board with Graham's proposal, however. The South Carolina Republican used his Sunday TV appearance to make a direct appeal to Sen. James Risch, R-Idaho, chairman of the Senate Foreign Relations Committee.

"Jim, if you're watching the show, I hope you are, let's call these people in. Eventually, we'll get to Hunter Biden," Graham said, referring to the former vice president's son. He added: "We're not going to let it go. Jim Risch, you need to start it."

Risch's office and the Senate Foreign Relations Committee did not immediately respond to requests for comment.

The crux of the impeachment case against Trump is whether he used $391 million in military aid, and a coveted White House meeting for Ukrainian President Volodymyr Zelensky, as leverage to force the foreign leader to conduct political investigations, including one focused on Joe Biden.

In a July 25 call, Trump asked Zelensky to "do us a favor."

Trump and administration officials repeatedly stonewalled House investigators, refusing to allow some witnesses to testify and to provide requested documents.

The House voted in December to impeach Trump, and in recent weeks, new evidence against him has emerged, including reports that former National Security Adviser John Bolton says there was a quid pro quo conditioning the aid on investigations by Ukraine that could help the president politically.

In an interview Sunday with Fox News host Sean Hannity, Trump said he has no plans to delay his annual State of the Union address, which is scheduled for Tuesday.

"No, I'm going to have it," Trump said in the interview, which aired on Fox before the Super Bowl. "It's going to be done. We're going to talk about the achievements that we've made."

He added that the impeachment process and the Russia probe led by former special counsel Robert Mueller were "unfair to my family."

"I mean, my family suffered because of all of this, and many other families suffered also," he said.

New e-mails

Over the weekend, the administration acknowledged the existence of two dozen e-mails that could reveal the president's thinking about withholding the aid to Ukraine.

Some Democrats had been looking to Alexander last week as a potential crossover vote in favor of subpoenaing key witnesses and documents in the Senate trial. But the Tennessee Republican said Sunday that while Trump's behavior was "inappropriate," it was "a long way from treason, bribery, high crimes and misdemeanors."

"I think he shouldn't have done it," Alexander said of Trump's alleged efforts to pressure Ukraine. "I think it was wrong. Inappropriate was the way I'd say — improper, crossing the line. And then the only question left is who decides what to do about that."

"Well, who decides what to do about that?" host Chuck Todd asked. "The people," Alexander responded.

On CNN's "State of the Union," Ernst said she, too, will vote to acquit the president.

Ernst, who is facing a tough re-election race this year, said she would not have handled the Ukraine matter in the way Trump did. But she offered only gentle criticism of his actions.

"Maybe not the perfect call," Ernst said, referring to Trump's oft-repeated claim that his phone conversation with Zelensky was "perfect." "He did it maybe in the wrong manner."

"I think he could have done it through different channels," such as the Department of Justice, she added.

House Speaker Nancy Pelosi and other leading Democrats have argued that any acquittal without the inclusion of witnesses and documents is meaningless — a point Senate Minority Leader Chuck Schumer re-emphasized ­Sunday.

"Senate Republicans keep voting for a sham trial without witnesses or documents," Schumer tweeted. "Make no mistake: The full truth will eventually come out, and Senate Republicans will have to answer for their coverup."