(CNN) -- Sunni Arab nations like Saudi Arabia, Kuwait and Jordan must pitch in on the rebuilding effort if Iraq is to witness progress and blend its Sunni population into the political fold, Sweden's foreign minister said Wednesday.
Swedish Foreign Minister Carl Bildt, right, greets Nuri al-Maliki on Wednesday at Arlanda Airport near Stockholm.
Carl Bildt spoke a day ahead of the International Compact with Iraq in Stockholm, Sweden. Mideast, U.S., Iranian and U.N. officials are among those attending the summit hosted by Iraqi Prime Minister Nuri al-Maliki.
Key to progress in Iraq, Bildt said, is "that the Sunni parts of the society move more clearly into the government structures."
"And that is going to be dependent, to some extent, I think, on the attitude that is taken by countries like Saudi Arabia, by Kuwait, by Jordan and others who have a stake in this particular process," Bildt told reporters, adding that the United States should also foster bilateral relations with such countries.
The agenda -- which will follow up on issues that were raised in the first international summit on Iraq in Sharm el-Sheikh, Egypt, last year -- will include discussions on debt relief, economic reconstruction, elections, corruption, the oil industry, the refugee crisis, security and political developments.
Bildt's comments reflect the concerns of the United States, which has long been pushing Sunni Arab governments to help Iraq financially and diplomatically.
Sunni Arabs prevailed politically under Saddam Hussein's regime, but were relegated when the dictator was toppled. Shiites and Kurds took the reins of government and Sunni Arabs dominated the insurgency. There have since been halting efforts to bring Sunnis into Iraqi politics.
The country's Iraqi Accord Front, the largest Sunni coalition, bolted from the government last year because it felt it was being marginalized by Shiites and Kurds. The coalition has expressed interest in rejoining the government lately, in part because the al-Maliki government launched military operations in Shiite regions.
Reidar Visser, a scholar of Iraq who is editor of the Iraq-oriented Web site historiae.org, said Sunni Arab states are unhappy with al-Maliki's leadership because he seems to favor a tripartite Iraq comprised of Shiite, Sunni and Kurdish regions.
Among Sunni Arabs' qualms with this philosophy is that there is no oil wealth in the Sunni heartland. The Kurds have a semi-autonomous region, many Shiites want their own and both want areas where there is abundant oil production.
"Should the Arab countries really open embassies in Baghdad and unconditionally cancel all debts? In the current situation, that would in practice mean bankrolling a system of government in Iraq based on ethno-sectarian regions, which few Iraqis are asking for," Visser wrote in a paper Wednesday called "The Stockholm Conference and Conditionality in Iraq."
In fact, Visser wrote, Arabs' standoffishness toward al-Maliki may be their last means of supporting Iraqis who dislike how "a small, foreign-sponsored parliamentary elite is ramming through a state model in Iraq that may well turn the country into an orifice of institutionalized sectarianism instead of a beacon of democracy in the region."
The State Department said much has been done to strengthen ties between Sunni Arab governments and Iraq, but more needs to be done, including increasing embassy presence in Iraq, expanding economic and commercial ties, and assisting security and diplomatic matters.
"There are not as many Arab embassies opened up or Arab ambassadors appointed to Iraq as we or the Iraqis would like to see. And vice versa: The Iraqis have an obligation, as well, to appoint ambassadors to these Arab states," State Department spokesman Sean McCormack said Tuesday.
However, he said, relations are better, citing Iraq's attendance at a Gulf Cooperation Council meeting.
Sideline bilateral meetings are common at such summits, and there has been speculation Secretary of State Condoleezza Rice could meet with her Iranian counterpart.
Bildt and McCormack are doubtful that will happen, but Bildt doesn't discount the possibility of lower-level meetings between the U.S. and the Islamic republic.
McCormack said talks on Iraq's economic relations with the rest of the world will be the centerpiece of the summit.
"The heart of the bargain is that Iraq will take certain steps in terms of laws it passes and the way it governs, and in return it will receive the benefits of a different kind of relationship with the rest of the world, whether that's in debt relief or debt alleviation or trade and investment," he said.
CNN's Elise Labott and Joe Sterling contributed to this report.