Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, speaks in Washington, D.C., Oct. 27, 2015. Andrew Harrer/Bloomberg via Getty Images

President Barack Obama will have the chance to decide on whether to increase the number of U.S. forces in Iraq in the "coming weeks," the top U.S. general said on Wednesday.

The extra troops would bolster the capabilities of Iraqi forces preparing for a major offensive against the Islamic State militant group in Mosul, U.S. Marine Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, told a news briefing.

U.S. and Iraqi military officials have been discussing a plan to retake Mosul, which fell to Islamic State in June 2014, and how U.S. forces could support their efforts, Dunford said.

"Those recommendations are being made and the president will have an opportunity to make some decisions here in the coming weeks," Dunford said. "I brought it to the secretary (Defense Secretary Ash Carter). The secretary will engage with the president."

Dunford said last week he expected an increase in the level of U.S. forces in Iraq from the current 3,800, but that those decisions had not been finalized.

U.S. officials have said they hope to capitalize on recent battlefield successes against Islamic State, such as the retaking of Ramadi by Iraqi forces late last year.

"The timing really now is focused on the next phase of the campaign, which is towards Mosul, and maintaining the kind of momentum that we had in Ramadi," Dunford said.