OSAGE, Iowa — Joe Biden said definitively on Wednesday that he would not participate in any witness swap as part of the Senate impeachment trial. His remarks came as other top Senate Democrats attempted to tamp down any notion that they would agree to call Biden or his son Hunter in return for appearances by top Trump administration officials.

Biden’s remarks, his most forceful attempt to signal that he wants no part of the impeachment trial in which Republicans are trying to embroil him, came after a voter here asked if he would offer to testify in return for testimony from people such as former national security adviser John Bolton or acting chief of staff Mick Mulvaney.

The former vice president said it was “not an irrational question to ask” but said that he would not engage in such a trade.

“The reason I would not make the deal, the bottom line is, this is a constitutional issue,” Biden said inside a VFW hall at the end of his latest Iowa swing. “We’re not going to turn it into a farce or to some kind of political theater. They’re trying to do that. I want no part of that.”

Biden said that if President Trump is not convicted by the Senate, he will emerge stronger and harder to beat, but that Congress had no choice but to move forward with impeachment.

“I’m not going to play his game,” Biden added. “The Senate job is now to try him. My job is to beat him.”

But the voter who asked the question was not fully satisfied with Biden’s response. Reflecting some of the tension within the Democratic Party over how the Bidens should fit into the impeachment hearings, the voter said he wished that Biden would testify.

“He should call the bluff. Trump is a bully and he needs to stand up to him,” said Stephen Delgado, a 70-year-old retiree from Surprise, Ariz., who drove to Iowa to see the candidates. “Democrats have to stop all this ‘When they go low, we go high.’ This is a street fight.”

He thinks that if Biden were to testify, it might help Democrats secure the testimony of Trump officials and give Biden a prominent platform to rebut Republican attacks.

“It would clear the air,” he said. “The people would get to see what a good, decent man he is.”

The possibility of Biden or his son offering their testimony has been one of the more fraught questions facing his campaign with less than two weeks to go before the Iowa caucuses. Earlier on Wednesday as he left an event in Mason City, Iowa, he rejected the idea that discussions were even taking place among Senate Democrats.

“No, they’re not,” he told a Washington Post reporter.

When told some were, he responded again, saying, “No, they’re not.”

Asked if he would consider testifying, he said a third time, “No, they’re not.”

The Trump impeachment trial focuses in part on the president’s effort to pressure Ukraine to investigate Biden and his son, who served on the board of a Ukrainian company while the vice president was the Obama administration’s point man on curbing corruption there. No evidence of wrongdoing by either Biden has emerged.

The Post reported Tuesday that several Democratic senators and aides have been discussing the possibility as a potential strategy during the Senate trial. Some of these people have suggested that the maneuver could end up benefiting Biden and would backfire on Republicans. The thinking among them was that Biden would forcefully reject any inference of wrongdoing and instead deliver a statesmanlike performance.

While some Democrats could still decide to join with Republicans to demand his presence, top Democrats on Wednesday rejected the idea of swapping witnesses.

“This isn’t like some fantasy football trade,” said Rep. Adam B. Schiff (D-Calif.), one of the House managers and the chairman of the House Intelligence Committee. “Trials aren’t trades for witnesses.”

Senate Minority Leader Charles E. Schumer (D-N.Y.) told reporters that he would also oppose the concept.

“I think that’s off the table,” Schumer said when asked whether he would agree to a trade of Hunter Biden’s testimony for that of Bolton’s. “First of all, the Republicans have the right to bring in any witness they want. They haven’t wanted to. And that trade is not on the table.”

Republicans have seized on the Bidens as they attempt to shift attention away from Trump’s actions. Sen Mike Braun (R-Ind.) said that he thinks Biden is the one Republicans should call to testify if there is a swap.

“You cannot have a free pass, at least to the point where you don’t look into it,” he said. “When I hear things like ‘conspiracy theory [that’s] been debunked,’ that’s a good sign that you need to look further.”

The former vice president on Wednesday launched into an extended defense of son Hunter. — whom Biden has been referring to as “my only surviving son” in reference to the death of elder Biden son Beau.

“No one has suggested my son did anything wrong,” Biden said.

He repeated earlier assertions that the sole problem with Hunter Biden’s employment by the Ukrainian company was the appearance of a conflict.

“There’s nobody that’s indicated there’s a single solitary thing that he did that was inappropriate, wrong . . . or anything other than the appearance. It looked bad that he was there,” Biden said. “He acknowledges that he in fact made a mistake going on the board.”

Biden, who has said that he did not make a mistake, went on to criticize Trump.

“Think about everything that President Trump does, from the time he got into real estate,” he said. “Whenever he has a problem, he blames somebody else. Tries to divert the attention.”

Biden has often struggled with how to respond to the scrutiny that comes with the Senate trial. Last month he told the Des Moines Register that he would not comply with a subpoena to testify in the impeachment trial, saying that doing so would allow Trump to shift the attention from his actions as president.

But amid harsh reaction for promising the same behavior Democrats were criticizing Trump administration officials for, Biden reversed course. He said that while he didn’t think there was a legal basis to call him to testify, he had “always complied with lawful order” and “cooperated with legitimate congressional oversight requests.”

“I would obey any subpoena that was sent to me,” he said in response to a voter question in Fairfield, Iowa.

Biden also blamed himself for allowing the story to fester.

“I shouldn’t even have answered the question,” he said. “Because in answering the question, now there’s going to be another round. We’re not talking about: What did Trump do?”

As he wrapped up three days of town halls in eastern Iowa, one of Biden’s rivals did his best to distance himself from the impeachment drama, inserting into his speech anecdotes meant to show his kinship with voters outside Washington.

“My focus is it’s not just about an ideological needle somewhere in Washington,” former South Bend, Ind., mayor Pete Buttigieg said in Dubuque. “At the end of the day, these ideas and these fights only matter because of what they’re going to do in everyday American life.”

Elise Viebeck in Washington and Chelsea Janes in Dubuque contributed to this report.