(CNN) -

After three years of seesaw battles with the regime, Syrian rebels now face another daunting challenge: fending off radical Sunni militants who are taking over swaths of the country.

The Islamic State in Iraq and Syria (ISIS) has gained notoriety in recent weeks as the group captured city after city in Iraq. Its goal: To create a caliphate, or Islamic state, spanning Iraq and Syria.

Now, the crises in both countries are blending into a combined regional disaster as ISIS now controls land on both sides of the border -- opening the floodgates for weapons and fighters between Syria and Iraq.

All the cities between Deir Ezzor city and the Iraq border -- a stretch of 90 miles (150 kilometers) -- have fallen to ISIS, said Omar Abu Leila, a spokesman for the rebel Free Syrian Army.

Deir Ezzor itself is controlled partly by the government and partly by opposition militants, he said.

That's not all. ISIS also took over six Syrian oil and gas fields and a major pumping station that distributes oil from Iraq into Syria, Abu Leila said.

The captures include the al-Omar oil field, Syria's largest oil facility that can produce 75,000 barrels of oil a day. ISIS has also seized a military airport and a local army base.

The land grabs by ISIS now stretch from Syria's Deir Ezzor province to the group's recently gained territories in Iraq's Sunni heartland, the opposition Syrian Observatory for Human Rights (SOHR) said.

While ISIS has controlled parts of Syria for some time now, the group was fighting to open a route between its captures in Iraq and in Syria.

That victory came Thursday, when ISIS wrested control of the Albu Kamal border crossing and all the cities between the crossing and Deir Ezzor city from Syrian rebels.

Some Syrians turn to ISIS

ISIS has gained not just cities, but also some Syrians' claims of allegiance.

After capturing the town of al-Shahil, ISIS demanded last week that fighters surrender their weapons and repent for fighting ISIS.

The militants then called on residents to leave the town for a week to 10 days until "peace returns to the streets," according to a social media video obtained by activists.

In a video statement, leaders in the town of al-Shahil announced their withdrawal from all anti-ISIS groups.

A town representative announced by video that they "decided to swear allegiance" to shadowy ISIS leader Abu Bakr al-Baghdadi.

But about 30,000 people have fled the town, Abu Leila said.

Other Syrians flee

Days after their land grabs across Deir Ezzor province, ISIS militants have not let residents return to the towns of Khsham and Tabyeh, the SOHR said.

About 15,000 people lived in each town.

The residents were forced to leave on June 23. They had been told to "accept their repentance" after fighting ISIS, the SOHR said.

ISIS militants have already declared they have set up an Islamic state spanning large areas of the two countries. The group called on Muslims to swear allegiance to the caliphate.

The message claims that the group's territory now spans from Aleppo province in northwestern Syria to Diyala province in eastern Iraq. It announced that ISIS was changing its name to just the "Islamic State."

But both Shia and Sunni Muslims have been deeply offended by the claim.

Syrian rebels demand help

A group of 11 battalions fighting ISIS in Syria has threatened to stop battling the insurgents by the end of this week if they don't get supplies and support from their Western-backed interim government.

The demand, posted on the Facebook page of one of the battalions, was addressed to the Syrian Coalition and the Syrian interim government -- both of which are Western-backed rebel groups fighting the Syrian regime.

"We ask for reinforcement and full support to face (ISIS), and expel them from our land, and stop them from advancing on the liberated cities," the statement said.

"If our call is not answered, we will be forced to lay down our weapons and pull our fighters from the areas we control."

Syrian Coalition spokeswoman Bayan Khatib relayed the group's demands to the media, saying ISIS is not only a threat to Syria, but to the West as well.

"The Free Syrian Army has made significant gains in Syria, but ISIS has consistently battled them for these areas and often won," Khatib said.

The demands come after ISIS made advances in Deir Ezzor and, more alarmingly, the suburbs of Aleppo -- Syria's largest city, Khatib said.

The rebels "have been screaming at the top of their lungs for months for assistance that never came," Khatib said. "In their statement, they predict that ISIS will take over all opposition territory in Syria unless decisive action is taken promptly."