The statement came after Mr Hongwei's wife, Grace Meng, told reporters how her husband "singalled he was in danger" by sending her an image of a knife.
'His job is very busy, ' she said.
Interpol is based in Lyon.
Meng, 64, who is also a senior Chinese security official, had more than 40 years' experience in criminal justice, particularly in the field of drugs control, counter-terrorism, immigration and border control, before becoming president of Interpol, the worldwide criminal police organisation based in Lyon, in November 2016.More news: Bucking party, Murkowski charts her own path on Kavanaugh
The websites of French papers broadcast video clips showing Grace Meng speaking in a trembling voice, with her back to a TV camera in order to hide her appearance.
In her first public comments on her husband's mysterious disappearance, Grace Meng said her husband sent her an image of a knife before he went missing.
China would have been well aware of those risks before acting in the way it did, Beijing-based political commentator Zhang Lifan said. She told police that she last heard from him 10 days prior and had received threats on social media and by telephone, according to the statement.
Earlier Sunday, at an emotional press conference in Lyon, Grace Meng spoke for the first time about his disappearance.
The 36-year-old took to China's Twitter-like Weibo to acknowledge her wrongs, beg for her supporters" forgiveness, and apologise to "society, the friends who care about me, the public and the national tax authorities'.More news: Interpol asks China for information on its missing president
Mr Meng, who is also China's vice-minister of public security, is one of a lengthening list of politicians, officials and celebrities to have fallen foul of... "If what Meng is involved in is nothing more than an ordinary corruption case, there would have been no need for the authorities to handle it in such a manner", he said.
Such targets, who have been subject to arbitrary detention and made unexplained disappearances, include pro-democracy activists, human rights lawyers, officials accused of graft or political disloyalty and the estimated one million ethnic minority Muslims who have vanished into internment camps in the country's far west.
She said she had not heard from her husband since this last message on September 25. He had been on a three-country tour, to Norway, Sweden and Serbia, for Interpol before his latest trip back to China, she said.
Meng has resigned "with immediate effect" and Senior Vice President Kim Jong Yang, a South Korean, has become acting president, the global police agency said in a statement.
Wong reported from Beijing.More news: US Senate heads to final vote on Kavanaugh Supreme Court nomination