Speaking to Korean troops stationed in Abu Dhabi last week, the South Korean president said his nation and the UAE are under "very similar" circumstances, each facing threats from North Korea and Iran.
"The security of our brother nation is our security," Mr Yoon said. "The enemy of the UAE, its most-threatening nation, is Iran, and our enemy is North Korea."
Bilateral relations between Seoul and Tehran had already been testy over frozen Iranian funds in South Korea and a suspected arms deal between Iran and North Korea.
Following Mr Yoon's remarks, which his office insists were intended as words of encouragement for South Korean soldiers, triggered a strong reaction from Iran, with its foreign ministry "investigating" the president's "interfering statements".
Seoul said it had offered explanations to Tehran.
South Korean first vice foreign minister Cho Hyun-dong called on Iranian ambassador Saeed Badamchi Shabestari on Thursday to explain Seoul's stance "once again".
The meeting was called in response to the summoning of South Korea's ambassador to Tehran by the Iranian Foreign Ministry on Wednesday, foreign ministry spokesperson Lim Soo-suk said in a briefing.
Mr Lim said the Iranian ambassador told the minister that he "faithfully" convey Seoul's explanation of Mr Yoon's comments to his bosses in Tehran.
"As we explained several times, (Yoon's) reported comments were meant to encourage our troops serving their duties in the UAE, and had nothing to do with Iran's foreign relations, including South Korea-Iran relations," Mr Lim said.
"Our government's will to develop relations with Iran remains unchanged."
The Iranian foreign ministry said it has lodged a strong protest over Mr Yoon's "meddlesome" remarks after summoning South Korean ambassador Yun Kang-hyeon.
During the meeting, deputy foreign minister for legal affairs, Reza Najafi, reportedly said that Mr Yoon's comments were "tantamount to interference" in what he described as Iran's "deep-rooted and friendly relations" with most Gulf states and undermined "peace and security in the region".
Mr Najafi also accused Seoul of pursuing an "unfriendly approach" toward Iran, and raised the issue of frozen funds. Iran has repeatedly demanded the release of nearly $7bn of its funds frozen in South Korean banks under US sanctions.
The South later said Mr Najafi had made a "completely groundless" claim that Mr Yoon had hinted at developing a nuclear weapon.
"Our president's remarks were intended to strengthen the effectiveness of the extended deterrence to counter North Korea's escalating nuclear and missile threats," the South Korean foreign ministry spokesperson.