If the Baghdad government can keep Sunni militants away from its oil fields, production in Iraq may actually increase—though global prices are still seen staying higher. Fear that Iraqi oil production could be disrupted by an insurgence by the militants has driven Brent futures up 5 percent in the past 10 days to about $115 per barrel. Iraq produces about 3.3 million barrels a day, and is OPEC's second largest—and fastest growing—producer. Citigroup analysts Thursday issued a new report saying the outlook for Iraqi oil is for more production, even with the clashes between ISIS and the Shiite-controlled Baghdad government. ISIS, or the Islamic State of Iraq and al-Sham, has seized a number of Iraqi cities, and was battling for control of the country's biggest refinery in the town of Baiji. The key to more production would also be a move by the Kurdistan Regional Government in the north—which has so far stayed mostly on the sidelines while Sunni and Shiite Arabs battle one another—to move toward sovereignty and take control of its own oil exports. Currently, Baghdad contests the Kurds' right to export crude, and some buyers have been reluctant to purchase from the Kurds for that reason. Read MoreHere are the best and worst case scenarios for Iraq

A member from the oil police force stands guard at Zubair oilfield in Basra, southeast of Baghdad June 18, 2014. Reuters

"Our base case is in the short run, we do get more oil. That base case is based on the Kurdistan Regional Government maintaining its independence and security and Baghdad maintaining its control over the southern oil field," said Edward Morse, head of global commodities research at Citigroup.

Citigroup says a fear premium could remain in the price of oil in the third quarter, but Morse said he does not expect to see a price of $120 a barrel for Brent unless more oil is taken off the global market.

Read More "There are cargoes of Angolan and Nigerian crude that nobody wants. The physical market is not as tight as the perception of a price going up by 4 percent. It's hoarding, in a way, and speculating," he said. "The physical market has not changed since before the taking of Mosul."

The energy industry, meanwhile, is meeting in Moscow this week at the World Petroleum Congress. Exxon Mobil Chairman Rex Tillerson was a keynote speaker. Exxon was reported to have moved most employees out of southern Iraq, but it has declined to comment on security issues.

Dan Yergin, vice chairman of IHS, was in attendance at the Moscow conference. He said that prior to the gathering, everyone expected the focus to be on Ukraine. Instead, it's shifted to the conflict in Iraq.

"The word here is that nothing (regarding production) has stopped, but everybody has contingency plans and is very focused on security even though they're a hundred miles away," he said. The global industry is also watching to see what the U.S. will do in response, he said. President Barack Obama on Thursday said military advisors would be sent to Iraq, but U.S. troops would not return to combat.

Yergin said talk at the conference is also centered on the idea that Kurdistan could move toward de facto sovereignty, and that its relationship with Turkey has been strengthened. "If this wasn't happening, one would be looking toward greater Iraqi production coming into the market. What this does is it gives the Kurds a freer hand to pursue their oil production, and in terms of seeking their sovereignty," he said. "The credibility of Iraq as a state is now at stake." The southern, Shiite-controlled oil fields are the richest in Iraq, and they currently produce about 2.6 million barrels a day. However, that number is projected to reach a record 2.8 million barrels by July, and 3 million by year-end, according to Citigroup. BP CEO Bob Dudley told CNBC this week that BP is actually increasing production in southern Iraq, at the request of the government, though nonessential personnel are leaving the country. Dudley was also at the World Petroleum Congress. Yergin said Lukoil was also expected to increase production in West Qurna in southern Iraq, where its production could reach as much as 400,000 barrels a day by the end of the year, up from 120,000 barrels a day currently. The northern part of the country around Kirkuk, now under Kurdish control, produces about 400,000 to 500,000 a day, according to IHS. Separately, the Kurdistan Regional Government-controlled area in northern Iraq exports about 125,000 barrels a day via a new Iraq-Turkey pipeline system and plans to increase exports to between 200,000 and 250,000 barrels a day during July, and up to 400,000 by year-end, according to Citigroup.

Morse expects to see the Kurds try to strike a deal with Baghdad on exports. "I tend to be optimistic on their being an agreement to do that before the end of the year, long before the end of the year," said Morse. According to Barclays, the huge Baiji refinery, out of commission because of fighting, and a nearby 1,320 megawatt power plant are responsible for one-third of Iraq's refined fuel and nearly 10 percent of its electricity capacity. The refinery is located 130 miles north of Baghdad. It's the northern region of the country that provides oil for domestic consumption, while about 90 percent of the oil from the Shiite-controlled south is exported, according to Barclays.

So far, the only reported disruption to the flow of oil out of Iraq is through the 600,000 barrel Kirkuk-Ceyhan pipeline, which runs from Kirkuk to Turkey. The pipeline has been out of commission for several months due to attacks by militants.

Read MoreIraq is on the verge of collapse: David Phillips

The Sunni-controlled regions of Iraq don't produce oil. The view of Citigroup Middle East analysts is that ISIS will not make much headway into the south of Iraq, or as far as Baghdad. Some experts see Iran, a close ally of the current Iraqi government, taking a bigger role militarily if Iraq's holy cities or capital are really threatened.