Top Obama administration officials reportedly are at odds over a newly announced agreement with Russia to curb the violence in Syria, with Defense Secretary Ash Carter voicing concerns about the plan announced by Secretary of State John Kerry.

The New York Times reported Wednesday on the friction. According to the article, Carter pushed back against the pact on a conference call with the White House last week, as Kerry grew frustrated.

President Obama approved the deal, but Pentagon officials still are not convinced.

On Tuesday, the U.S. Air Force general charged with running the air war against the Islamic State was asked if he trusts the Russians.

“I'm not going to tell you I trust them. I think, from our side, [we] have to do some planning and they need to do the right thing.  We'll see what happens from there," Lt. Gen. Jeffrey Harrigian said in a video conference at the Pentagon from his headquarters in Qatar.

When asked if the U.S. military was prepared to start working with Russians the day after a new cease-fire ends, Harrigian said, “That's going to depend on what the plan ends up being.”

Confusion remains over the terms and aims of the deal, as well as the interim cease-fire deal.

On Monday, Kerry initially said the United States and Russia could permit President Bashar Assad's government to launch new airstrikes against Al Qaeda-linked militants under the arrangement. The State Department quickly reversed itself.

Spokesman John Kirby said later there were no provisions under the nationwide truce for U.S.-Russian authorization of bombing missions by Assad's forces. "This is not something we could ever envision doing," he said.

Kerry's comments at a news conference were the closest any American official had come to suggesting indirect U.S. cooperation with Assad since the civil war started in 2011. President Obama called on Assad to leave power more than five years ago; the U.S. blames the Syrian leader for a war that has killed perhaps a half-million people.

Meanwhile, Russian and Syrian regime jets continue bombing opposition groups in Syria, albeit at reduced levels, two U.S. officials with knowledge of the recent intelligence in the region told Fox News.

This raises new questions about what level of violence will be accepted by the Obama administration in determining whether to go ahead with the proposed joint venture with Russia after a week-long ceasefire, which includes the sharing of intelligence at a joint intelligence center.

Under the truce that went into effect at sundown Monday, Assad's forces are no longer supposed to bomb Syria's opposition, Kerry said earlier.

On Tuesday, though, a senior administration official pointed merely to “reduced violence” – as opposed to a complete “cessation” – arguing the reduced violence could bring about military cooperation between the U.S. and Russia in Syria.

If the relative calm holds for seven days, the U.S. and Russia would then cooperate on how to jointly combat the Al Qaeda-linked group formerly called the Nusra Front and now known as Jabhat Fatah al-Sham.

Various militants backed by the U.S. and its Arab allies coordinate and even sometimes fight alongside Al Qaeda-linked militants. Many Syrian and Russian operations have struck what U.S. officials describe as "moderate" forces that are "marbled" with the militants.

The new cease-fire is supposed to end such ambiguities, and Washington has been urging rebel groups to break ranks with extremists.

Fox News’ Lucas Tomlinson and The Associated Press contributed to this report.