Hathurusinghe was under pressure to quit after Sri Lanka's dismal showing in the recent World Cup.
The island nation won just three preliminary round games and failed to make it to the semifinals. However, after returning to the country, Hathurusinghe said he was keen to continue until the expiry of his contract, which was until the end of the next year.
The 51-year-old was appointed in December 2017 after he left his job with the Bangladesh team. However, he was not able to turn around Sri Lanka's dismal performances and the team lost 13 out of the 20 ODIs played in the run-up to the World Cup under his charge, which left them at No.8 in international rankings.
Sources said Hathurusinghe was expected to return to coaching Bangladesh after the sacking of Steve Rhodes by that team.
Sports Minister Harin Fernando had earlier announced that he expected the entire Sri Lankan coaching staff to step down, taking responsibility for poor World Cup performance.