BAGHDAD, Iraq (CNN) -

U.S. Secretary of State John Kerry met Iraqi leaders Monday as radical Sunni militants continue their march toward Baghdad during the country's tensest time since the U.S. withdrawal of troops in 2011.

"The future of Iraq depends on decisions made in the next few days and weeks," Kerry said after meeting with Iraqi Prime Minister Nuri al-Maliki, the man who some observers say needs to step down.

Al-Maliki has agreed to a July 1 deadline to begin the process to form a new government, a requirement for U.S. assistance in fighting the Islamic State in Iraq and Syria, or ISIS, Kerry said.

"Our support will be intense, sustained," and will be effective if Iraqi leaders unite to face the militant threat, he said.

With al-Maliki's Shiite-led government losing more ground to ISIS, Kerry implored the leader to rise above "sectarian motivations" to become more inclusive and make the government more representative of Iraq's population.

Kerry also met with Iraq's foreign minister as well as Shiite and Sunni leaders.

Al-Malaki's office issued a statement after his meeting with Kerry, saying the Prime Minister told Kerry the current situation "poses a threat" not only to Iraq but the region as well. Al-Malaki "called on the countries of the world, especially countries in the region, to take it seriously," the statement said.

But outside the rooms of high-level talks, parts of Iraq are falling by the day. Here's the latest on the crisis that is spilling far beyond Iraq's borders:

Where is Iraq's military?

The United States believes "multiple Iraqi military divisions" outside Baghdad have dissolved and are plagued by problems in morale, leadership, training and equipment, according to a senior U.S. defense official.

"The readiness outside of Baghdad is certainly in question as they have ceded multiple towns. Forces in Baghdad seems to be holding today," the official said.

The United States believes there are around 10,000 fighters who are either affiliated with ISIS or members of the group, the official said, and while they are stretched thin over vast territory, they are getting support in the Sunni areas they increasingly control.

Kerry said Monday in Baghdad that President Barack Obama has prepared "a range of options for Iraq," including enhanced intelligence, joint operations centers, military advisers and "steady supplies of munitions."

But the United States is being more careful about sending additional weapons and ammunition to Iraq, because of a lack of confidence in the Iraqi troops, the defense official said.

ISIS captures more ground

Militant fighters believed to be ISIS have seized the Baiji oil refinery, the largest in Iraq, three Iraqi security sources told CNN Monday.

Earlier in the day, an Iraqi military spokesman had said that an attack was under way, but had been repelled by security forces. CNN cannot independently confirm either claim.

The Baiji refinery is a key strategic resource because it refines much of the fuel needed for internal consumption. There are already long lines at many gas stations across the country.

ISIS militants also advanced toward Baghdad over the weekend from the north and the west. At least 70% of Anbar province is now under the control of ISIS, two security officials in the region told CNN.

ISIS is on a mission to create an Islamic state across Sunni areas of Iraq and in Syria.

Militants have taken over the Tal Afar airbase in northern Iraq as well as the city of Tal Afar, officials said.

On Monday, Iraqi troops prepared to recapture the airbase, Iraqi Maj. Gen. Abu al-Waleed said. "At least 1,000 Iraqi troops have amassed to the north of Tal Afar and are firing rockets at militants in control of the city," he said.

The fighters also seized the western Anbar town of Rutba, 70 miles (113 kilometers) from the borders of Jordan and Saudi Arabia, security sources in Baghdad and Anbar told CNN on Sunday.

Then there's Qaim. ISIS captured the city along the Syrian border Saturday, and the militants now enjoy a stronghold and a number of other towns in Anbar province. The fighters have a direct line to the western outskirts of Baghdad, where tension simmers just beneath the surface.

Checkpoints in the capital seemed to pop up overnight, particularly the closer one got to central Baghdad. Security forces appeared to be controlling access to neighborhoods through a mix of checkpoints and road closures.