"I am asking you to consider my resignation, and discuss the issue in my absence," the country's parliamentary speaker quoted the minister as saying on Tuesday.
German media said airport officials refused to allow Lutsenko and his 19-year-old son to board a flight to Seoul, South Korea, on May 4 as they were both extremely drunk and behaving inappropriately. They were then reported to have been arrested after fighting with and injuring police officers who were called to the scene.
The country's largest opposition party Party of Regions demanded Lutsenko's resignation over the scandal. However, the Interior Ministry said the accounts of the incident were based on media reports and were not true. While Lutsenko has also claimed German police apologized to him for the incident, he also admitted that his position was now impossible.
"Considering that the smear campaign against me and my son is continuing, I understand how difficult it will be for me to carry on the duties of interior minister," Lutsenko said.
He also said the "incident" had been used by opponents pursuing their own interests amid ongoing domestic political disputes.
