Biden's surprising statement came on Monday during an interview with CNN television, Today's Zaman reported.
The seasoned politician has been the target of criticism in his country due to his political gaffes.
"Look, what I learned is, I'm not changing my brand. There's nothing I've said that I haven't said that was truthful. And so sometimes -- you know, everybody says they're looking for authenticity," he told.
Stressing that he does not offer apologies even when his words offend people, Biden gave the example of his exchange with Erdoğan.
"I never apologized to him. I know him well. I've dealt with him. I called him and said, 'Look, what was reported was not accurate to what I said," said Biden.
Biden indicated in a speech at Harvard University's John F. Kennedy School of Government on Oct. 2 that US allies in the region, including Turkey, Saudi Arabia and Qatar, contributed to the rise of the "Islamic State" (IS) and that Erdoğan, whom he called an old friend, had told him that Turkey had "let too many people through," even though Turkey is now trying to secure its border.
Erdoğan denied ever making such a statement and told reporters in Istanbul before Biden's reported apology that the vice president would "be history for me if he has indeed used such expressions."
Turkey has been accused by Western officials and media in the past few years of turning a blind eye to foreign fighters crossing into Syria via Turkish territory to join IS.
Biden called Erdoğan on Oct. 4 and he "apologized for any implication that Turkey or other allies and partners in the region had intentionally supplied or facilitated the growth of IS or other violent extremists in Syria," the White House said.
After the White House statement, pro-government Turkish media outlets touted that Biden had to finally apologize to Erdoğan for what he said.
White House Press Secretary Josh Earnest said Biden had called Erdoğan and apologized for any implication that Turkey helped radical groups as well. "What the vice president conveyed was an apology for -- as it relates to President Erdogan -- mischaracterizing the president's views in a private conversation," Earnest said, adding, "And that, ultimately, was the reason for the call."
"I think the vice president was pretty candid about why he owed President Erdoğan an apology, because he had mischaracterized his private remarks," Earnest said at that time.
"The vice president is somebody who has enough character to admit when he's made a mistake," Earnest told reporters.
"[Biden] is somebody who continues to be a core member of the president's national security team. He is somebody who has decades of experience in dealing with leaders around the globe. And the president is pleased to be able to rely on his advice as we confront the variety of challenges that are so critical to American national security."
Speaking following Biden's speech, Prime Minister Ahmet Davutoğlu said, "This is really a very unfair accusation," when asked what he thought about Biden accusing Turkey of supporting IS against Assad. Davutoğlu also said Turkey wants "fairness and empathy."
Turkey has prioritized the removal of the Assad regime in Syria rather than focusing on the immediate threat of IS. Turkish officials view the Assad regime as the main factor in the creation of an environment that enabled the emergence of radical groups such as IS. But the US and other Western countries have made clear that removing the Assad regime from power is not a priority.
Asked about the discrepancy on Monday, Biden's office only said that there had been a "genuine misunderstanding" about Biden's speech, repeating its earlier explanation that Biden never intended to imply Turkey had helped IS, according to the Associated Press (AP). Biden's office wouldn't comment to the AP about whether it stood by its earlier statement that Biden had apologized.
The vice president's office also said Biden was still looking forward to meeting with Erdoğan this month.
Biden is scheduled to visit Turkey in mid-November to meet with Turkish officials at a time when the two NATO allies' relationship is struggling due to how to deal with IS. According to the White House, Biden will travel to Morocco, Ukraine and Turkey during the week of Nov. 17. He is expected to meet with Erdoğan, Davutoğlu and representatives of nongovernmental organizations.
The US has been pushing Turkey to contribute more to the US-led coalition against IS. Ties between the US and Turkey have been strained, as the US is asking for more access to Turkey's İncirlik Air Base to launch military strikes against IS targets inside Syria.
Biden has a reputation for verbal missteps in foreign policy. He is considered a potential presidential candidate in 2016.
According to the Turkish news portal Diken, a source close to the White House said Biden's surprising statement denying that he has apologized to Erdoğan is a deliberate, calculated move before Biden's visit to Turkey. The source claimed that Biden's statement aims to set the tone and render Erdoğan ineffective before Biden's visit in mid-November.