(CNN) -

The back-and-forth continued Wednesday on the battlefield, across the political spectrum and in the skies over Iraq, where the simmering unrest shows no sign of abating.

Here are some key developments over the course of the day:

U.S. military advisers begin work

U.S. military advisers are in Iraq, and they sat down with Iraq's various security forces, said Iraq's military spokesman, Maj. Gen. Qassim Atta.

"The advisers have been distributed in groups to the Defense Ministry, the Interior Ministry, the Baghdad operations center and the counterterrorism unit," Atta said.

Ninety of the 300 advisers promised by U.S. President Barack Obama arrived this week, and another 40 working the U.S. Embassy have been reassigned to advise, the Pentagon said earlier this week.

The road to Samarra

Security forces control the road from Baghdad to Samarra, home of a revered Shiite shrine, Atta said during a televised briefing.

"We are continuing the operation to cleanse Samarra" province, he said.

Samarra sits 100 kilometers (62 miles) north of Baghdad, and is significant to Shiites for its al-Askari mosque. ISIS fighters, who are receiving support from Sunni tribes, have threatened to destroy any shrine they deem un-Islamic.

An attack on the mosque in 2006 was ground zero for the sectarian fighting that pushed the country to the verge of civil war, and many fear another such attack would push Iraq to the breaking point.

Kirkuk car bomb

A car bomb exploded at an outdoor market in northern Kirkuk on Wednesday, killing at least six people and wounding 21, police officials told CNN.

The explosion occurred in the predominantly Kurdish neighborhood of Rahimawa, the officials said.

Kirkuk is an ethnically mixed city of Sunni, Shiite, Kurds and Turkmen, who all lay claim to the oil-rich city that sits 260 kilometers (162 miles) north of Baghdad.

Kerry on Iran's involvement

U.S. Secretary of State John Kerry declined to comment on Iran's intention toward Iraq, saying, "Frankly, you should best direct that question to Iran and the government of Iraq.

"But from our point of view we have it clear to everyone in the region that we don't need anything to take place that might exacerbate the sectarian divisions that are already at a heightened level of tension, and so it is very important that nothing takes place that contributes to the extremism or could act as a flashpoint with respect to the sectarian divide," Kerry told reporters.

The secretary's comments come as the conflict in Iraq has widened amid reports of Syrian airstrikes and Iranian involvement.

"It's been widened obviously in the last days with the reports of IRGC personnel, some people from Iran being engaged in Iraq, with perhaps even some Syrian activities therein, and that's one of the reasons why government formation is so urgent," he said.

"...President Obama is very, very clear that our priority is that government formation, and we are going to take every step we can over the next days."

A U.S. official told CNN that Iran is flying surveillance drones over Iraq. Iran is believed to be providing small arms and ammunition to Iraq, as well as providing intelligence to the government, the official said.

Syrian airstrikes

Reports that Syrian warplanes conducted a cross-border attack on Iraqi towns this week is further evidence of the blurring between the two countries' borders as they face an offensive by Islamic extremists.

At least 57 Iraqi civilians were killed and more than 120 others were wounded by what local officials say were Syrian warplanes that struck several border areas of Anbar province Tuesday.