Regulators determined that the woman, Matsuri Takahashi, worked excessive hours in her position at Dentsu, clocking 105 hours of overtime in the month preceding her death.
In September, the Japanese government ruled that Ms Takahashi's death had been caused by overwork.
According to the paper, 22.7% of companies polled between December 2015 and January 2016 said some of their employees logged more than 80 hours of overtime each month - the official threshold at which the prospect of death from work becomes serious.
According to The Japan Times, Ishii told a Tokyo press conference yesterday: "We deeply regret failing to prevent the overwork of our new recruit".
The bulk of inspections, which looked into cases of Dentsu employees' karoshi - death from overwork - as well as work-induced psychological problems, were carried out after June 2014 and before Takahashi's death.
"This is something that should never have been allowed to happen", Mr Ishii said.
Dentsu - which reduced its overtime cap from 70 hours a month to 65 hours in November - acknowledged that a successor will be named after the board meets, but did not specify a date.
Police seize $360m in cocaine in Sydney Fish Market and Tahiti raids
In July 2014, the Australian Federal Police and NSW Police Force State Crime Command's Drug Squad commenced Operation Okesi. On Christmas day, Australian officials seized 1102 pounds of cocaine in the nation's largest drug bust in its history.
His announcement came just a day after the Tokyo Labor Bureau said it will be referring the company and one of its executives to prosecutors, on suspicion that the suicide of a worker in 2015 had resulted from their violation of Japan's labor law.
She jumped to her death in December a year ago and in a note left for her mother, she asked: "Why do things have to be so hard?"
It started turning off headquarters lights at 10 pm so workers would go home.
During investigations into allegations such as illegally long working hours, the company received five warnings for excessive overtime hours, the sources said, hinting the firm could have dragged its feet in improving conditions for staff.
Ichiro Oshima, a 24-year-old Dentsu employee, killed himself in 1991 in Japan's first recognised case of karoshi-related suicide. Officially defined, karoshi includes both suicides and cardiovascular-related deaths, following periods of intense overtime.
The Japanese government a year ago approved a law to address problems caused by excessive work, but the lack of rigor on recording of extra hours by firms, and the staff's willingness to extend their working hours to earn a bonus makes it hard to control the practice.