(CNN) Former US special envoy to Ukraine Kurt Volker said Tuesday he failed to realize that an investigation into the Ukrainian energy company Burisma Holdings was linked to a probe of President Donald Trump's political rival, former Vice President Joe Biden, which Volker now says was "unacceptable."

Volker testified as part of the House impeachment inquiry that since his prior closed-door testimony, he had learned of conversations others had linking a White House meeting and US security aid with the Ukrainian President announcing an investigation into the Bidens.

Volker's testimony is a key component of the House's inquiry, as he was part of the trio who met with Trump on Ukraine policy and worked directly with Trump's personal attorney Rudy Giuliani to help Ukraine draft a statement on investigations.

Republicans have seized on his earlier testimony, in which he said he saw no evidence of a quid pro quo conditioning US security aid and a one-on-one meeting on an investigation.

But Volker, the first witness behind closed doors in the House's impeachment inquiry, said Tuesday that since his initial testimony "a great deal of additional information and perspectives have come to light."

"I have learned many things that I did not know at the time of the events in question," he said. "I did not know of any linkage between the hold on security assistance and Ukraine pursuing investigations. No one had ever said that to me -- and I never conveyed such a linkage to the Ukrainians."

Volker testified Tuesday afternoon alongside former National Security Council senior aide Tim Morrison, who listened to the July 25 call between Trump and the Ukrainian President. Their testimony followed a morning hearing for impeachment investigators with two other officials who were on the July call: National Security Council Ukraine expert Lt. Col. Alexander Vindman and Jennifer Williams, an aide to Vice President Mike Pence. Volker is a key witness for Democrats leading the impeachment inquiry because, as a former State Department official, he provided the committee with text messages documenting conversations he had with US diplomats, Giuliani and a top Ukrainian political aide.

Volker was involved in an effort with Giuliani, US Ambassador to the European Union Gordon Sondland and the aide to Ukrainian President Volodymyr Zelensky, Andriy Yermak, in crafting a statement for Zelensky to deliver that would satisfy Trump's concerns.

After Giuliani proposed including specific references to "Burisma and 2016," Volker said, the Ukrainians said they did not want to go forward with the statement. Volker said he thought the matter was then dropped -- which was not the case.

"These were the last conversations I had about this statement, which were on or about August 17-18. ... At this time, I thought the idea of issuing this statement had been definitely scrapped," Volker said. "In September, I was surprised to learn that there had been further discussions with the Ukrainians about President Zelensky possibly making a statement in an interview with US media similar to what we had discussed in August."

While Volker diverted from his initial testimony, Republicans pointed to him having no evidence of a quid pro quo involving the President. Rep. Mike Turner, an Ohio Republican, argued that none of the witnesses who had testified thus far had heard from the President that aid or a White House meeting was conditioned on investigations.

"Did the President of the United States ever say to you that he was not going to allow aid to the United States to go to Ukraine unless there were investigations into Burisma, the Bidens or the 2016 election?" Turner asked.

"No, he did not," Volker said.

One of the conversations Volker was unaware of was when Sondland spoke to an aide to Zelensky on September 1 following a meeting between Vice President Mike Pence and Zelensky. In the side conversation, Sondland has said, he told the Ukrainian aide that the US security aid would be released if Zelensky announced the investigation.

That conversation was only revealed after Sondland amended his testimony, saying he had recalled it after his deposition. Sondland testifies publicly on Wednesday.

Morrison is another witness who, like Volker, Republicans requested for public testimony. Unlike the witnesses who testified Tuesday morning, Morrison had said in his closed-door deposition that he did not have concerns, like Vindman and Williams had expressed, about the content of the call, but he did express concerns about the potential that it could have leaked. Morrison disagreed with Vindman's statement that Trump had demanded Zelensky investigate the Bidens, as Vindman had testified earlier Tuesday.

"As I stated during my deposition, I feared at the time of the call on July 25 how its disclosure would play in Washington's political climate. My fears have been realized," Morrison said Tuesday in his opening statement.

Testimony adds to questions about Sondland's testimony

At the same time, Morrison's closed-door deposition corroborated the account of Bill Taylor, the top US diplomat in Ukraine, that he was told US security aid had been conditioned on the opening of an investigation into former Vice President Joe Biden and his son Hunter Biden.

Morrison recounted under questioning from Democratic counsel Daniel Goldman how Sondland told him about the conversation he just had with Yermak on the sidelines of Pence's September 1 meeting with Zelensky in Warsaw. Sondland said that "the Ukrainians would have to have the prosecutor general make a statement with respect to the investigations as a condition of having the aid lifted," Morrison testified, adding that he was concerned it was creating another "hurdle" to Ukraine receiving the security assistance.

A week later, Morrison said that Sondland told him about his conversation with Trump in which the President said there was no "quid pro quo" with Ukraine but that Yermak had to announce the investigations.

"I understood that's what Ambassador Sondland believed," Morrison said of Sondland's comments.

"After speaking to President Trump?" Goldman asked.

"That's what he represented," Morrison responded.

The conversation is one of several instances in which Sondland is expected to face questions about his initial testimony.

Volker testified Tuesday that he did not understand that the push to investigate the Ukrainian natural gas company Burisma was actually a reference to investigating Biden and his son Hunter. Hunter Biden sat on the board of directors for Burisma Holdings.

"As you know from the extensive, real-time documentation I have provided, Vice President Biden was not a topic of our discussions," Volker said. "In hindsight, I now understand that others saw the idea of investigating possible corruption involving the Ukrainian company Burisma, as equivalent to investigating former Vice President Biden. I saw them as very different -- the former being appropriate and unremarkable, the latter being unacceptable."

Volker added: "In retrospect, I should have seen that connection differently, and had I done so, I would have raised my own objections."

Allegations against Biden 'not credible'

Volker said he told Giuliani that the allegations being made about the Bidens were "not credible," and that Biden would not "have been influenced in any way by financial or personal motives in carrying out his duties as vice president."

But Volker was tapped, along with Sondland and Energy Secretary Rick Perry, to head up Ukraine policy and work with Giuliani to satisfy Trump's concerns. Volker was present at a July 10 meeting when Sondland raised the notion of Ukraine announcing investigations to secure a meeting with Trump. But Volker said that he "may have been engaged in a side conversation, or had already left the complex" when he didn't hear Sondland talking about the meeting being conditioned on the investigations.

Volker said Tuesday he recalled that Sondland raised "generic" investigations with the Ukrainians at the formal meeting with then-national security adviser John Bolton, who cut off Sondland and ended the meeting, prompting Sondland to take the Ukrainians to a side room, where he linked the investigations to the White House meeting.

House Intelligence Chairman Adam Schiff pressed Volker on why that wasn't included in his initial testimony last month. "I did not remember that at the time of my October 3rd testimony," Volker responded. "I read the account by Alex (Vindman) and that jogged my memory, yes, that's right, that did happen."

Volker also said he had not been aware of Sondland's July 26 phone conversation with Trump, in which others have testified that Trump asked Sondland if Zelensky was going to do the investigations, and Sondland said Zelensky was ready to move forward.

Volker was questioned about the text messages he exchanged involving Giuliani, Yermak, Sondland and Taylor. In those texts exchanged in mid-August, Sondland and Volker worked with Yermak to try to draft a statement on investigations that they hoped would ease the concerns Giuliani and Trump had expressed. Volker said that the initial statement on investigating corruption was already something Ukraine was doing so there were no issues. After Giuliani suggested adding 2016 and Burisma to the statement, Yermak said they were uncomfortable with the notion, and Volker said the statement was ultimately dropped.

But Volker didn't realize at the time that Giuliani was pushing for a statement on investigating Biden — or that Sondland continued to push the effort weeks afterward.

Volker also dismissed a term that has become part of the Ukraine lexicon — the "three amigos" nickname that had been used by Sondland to describe Sondland, Perry and Volker, the three officials who were leading Ukraine policy.

"I never used that term -- and, frankly, cringe when I hear it," Volker said. "Because for me, the 'three amigos' will always refer to Sen. John McCain, Sen. Joseph Lieberman and Sen. Lindsey Graham."

This story has been updated with additional developments Tuesday.