Speaking at a U.S. Institute of Peace conference this week, Petraeus warned that Afghan violence would increase dramatically without such an intensified commitment by the international community, The New York Times said Friday.
A lack of additional efforts in Afghanistan by the United States and other countries could also lead to a resurgence in power by al-Qaida and the Taliban, the general said Thursday.
Petraeus did not offer a timetable for that potential increase in Afghan efforts, the Times said.
The military official also said Iran and other countries, including the United States, had similar interests in Afghan stability.
Petraeus did hint during Thursday's ceremony in Washington that such shared interests could make related talks with Iran a possibility, the Times reported.