President Yoon Suk-yeol, left, and Japanese Prime Minister Fumio Kishida pose for a photo prior to their talks in New York on Sept. 21, as they meet on the sidelines of the U.N. General Assembly. Yonhap

Korean President Yoon Suk-yeol wound up his second overseas trip amid embarrassment over the use of foul language caught on hot mic, but the trip was marked by one unmistakable outcome: the first summit with Japan in nearly three years.

Yoon began the trip with a stop in London to attend the state funeral of Queen Elizabeth II, an occasion that also provided the president with the opportunity to meet with new King Charles III and mingle with other leaders who had flown in from across the world.

Despite the solemnity of the events surrounding the funeral, Yoon, whose approval ratings tumbled to the 20 percent range in the summer, took another hit from critics at home after he was forced to postpone signing a condolence book for the queen.

Yoon's office said the signing was postponed from Sunday to Monday, the day of the funeral, per the instructions of the British royal family, given traffic conditions in London that made it difficult for all the visiting foreign leaders to travel to Westminster Hall at the same time.

But critics claimed Yoon had been snubbed by the British royal family and that leaders from the Group of Seven nations had received proper care in accordance with diplomatic protocol.

Yoon's second stop was New York, where the president spent the largest portion of his seven-day trip to attend the U.N. General Assembly, hold a series of bilateral summits on the sidelines, and meet with diverse groups of people, including students, Korean American scientists and global business leaders.

In previewing the trip, the presidential office had picked three highlights: Yoon's first address to the U.N. General Assembly, the first bilateral summit between South Korea and Japan in nearly three years, and a second summit between Yoon and U.S. President Joe Biden.

The South Korea-Japan summit, in particular, raised hope of a breakthrough in relations badly frayed over wartime forced labor and other issues related to Tokyo's 1910-45 colonial rule of the Korean Peninsula.

The summit with Biden was also seen as an opportunity to deliver South Korea's concerns about the U.S. Inflation Reduction Act (IRA), which is feared to put Korean carmakers at a disadvantage in the American market, and move forward discussions on a potential currency swap deal that could help stabilize financial markets.

What played out, however, was a tug of war between South Korea and Japan over whether the summit would be held at all, with the end result being a 30-minute meeting described by South Korea as "informal talks."

The summit took place suddenly, as the details had been kept under wraps for days, in the form of Yoon visiting the venue of an event hosted by Japanese Prime Minister Fumio Kishida in New York.

Yoon and Kishida "agreed on the need to improve bilateral relations by resolving pending issues," South Korea's readout of the meeting said. The two agreed to instruct their diplomats to accelerate talks to that end.

Yoon and Kishida also "shared serious concern about North Korea's nuclear program," including its recent legalization of nuclear arms and the possibility of a seventh nuclear test, and "agreed to cooperate closely with the international community to respond to it," according to the readout.

President Yoon Suk-yeol, center, talks with U.S. President Joe Biden, left, after attending the seventh replenishment conference of the Geneva-based Global Fund to Fight AIDS, Tuberculosis and Malaria in New York on Sept. 21. On the right is Foreign Minister Park Jin. Yonhap

A presidential official hailed the summit as "the first step toward producing tangible results."