The photographs published by Spanish publication Lecturas, showed the former handball player, 54, walking along a beach with a woman now revealed to be his co-worker at Imaz&Asociados law firm - Ainhoa Armentia.
Iñaki was captured by the media arriving at his office in Vitoria on Thursday morning, where he was asked about the photographs published by the Spanish magazine.
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"Things happen and we are going to manage it in the best possible way," he told the press.
When asked about how his family is, he added: "We will manage [the situation] with the utmost calm and together, as always."
Ainhoa arrived at the office shortly after Iñaki and declined to comment.
Meanwhile, the couple's second son, Pablo Urdangarin, 21, told the press: "We are all going to love each other the same."
Iñaki and Infanta Cristina pictured in 2019
Iñaki and Infanta Cristina were last pictured publicly together last month in photos published by HOLA! as they enjoyed a family holiday in Baqueira Beret. The couple, who married in 1997, share four children, Juan, Pablo, Miguel and daughter Irene.
In June 2018, Iñaki was given a five year and ten-month prison sentence following convictions of embezzlement and money laundering in excess of £4.5 million through his non-profit organisation, the Noos Institute.
Last year, Iñaki was granted permission to move to Spain's tercer grado or Grade 3 prison regime, meaning that he only reports to prison once a week.
Infanta Cristina was also investigated but acquitted of any charges. However, King Felipe issued a decree stripping his sister of the title of Duchess of Palma in 2015.
She is the youngest child of former King Juan Carlos I and Queen Sofia, and remains sixth in line to the throne behind her older sister, Infanta Elena, Duchess of Lugo, and her two children.
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