It seems Amiri and some other PMU leaders are serious about rapprochement with the United States. This, however, has earned Amiri some criticism. Aws al-Khafaji, the head of the Abu al-Fadl al-Abbas Brigades, made scathing comments against Amiri, saying, “Protesting [against the US Embassy move to] Jerusalem does not go hand in hand with a meeting with the American ambassador.”

On June 4, the Fatah Alliance invited several foreign ambassadors for iftar, the nightly fast-breaking meal during Ramadan. Photos from inside the alliance headquarters showed a meeting between alliance leader Hadi al-Amiri and US Ambassador to Iraq Douglas Silliman. Other ambassadors also were present.

It has been the custom for protesters every year on Quds Day — and other occasions — to trample and burn the Israeli and American flags. This year, however, no American flags were destroyed or burned, and the protests did not include any slogans or threats against the United States.

Some militias of the Iran-backed, mostly Shiite, Popular Mobilization Units (PMU) in Iraq seem to be working to end the hostility toward Washington. Some indication of this was seen during the recent International Quds Day protests, which were organized by armed Shiite factions close to Iran in the Iraqi capital of Baghdad. The rallies were held June 8, marking the last Friday in the holy month of Ramadan, to show support for the Palestinian struggle against the Israeli occupation. The Quds Day protests are an annual tradition that started in 1979 by Ayatollah Ruhollah Khomeini, the late leader of the Islamic Revolution.

Many Shiite armed factions in Iraq haven't been threatening the United States of late, especially since they fared so well in the May 12 elections, receiving the second-most number of parliament seats. The shift indicates a possible rapprochement between the two sides, albeit undeclared.

Karim al-Nouri, a close Amiri associate, hinted that the PMU's influential Badr Organization hasn't ruled out any rapprochement or dialogue with the United States.

“There is no conflict between the PMU or any foreign state. The Jerusalem [Quds] Day is a public celebration, where people are free to express themselves the way they want to,” Nouri told Al-Monitor. “Not destroying the American flag doesn't suggest good relations. Burning flags during protests doesn't mean that [Iraq] is on the outs with [the United States]. We only have reservations about Israel.”

On the same day Silliman visited Amiri, he also met with the leader of the State of Law Coalition, Iraqi Vice President Nouri al-Maliki, who more than once has attacked the United States. Maliki is a PMU leader and claims to be its founder.

Silliman’s keenness to meet two PMU “leaders” in a single day is further evidence that the United States has been looking at some PMU principals as possible partners.

The United States doesn't deal with the PMU as a whole institution, but rather with each faction separately. The United States is closest to Amiri, who in addition to leading the Fatah Alliance also heads the Badr Organization. “Amiri has been in contact with the United States via ongoing meetings in Baghdad,” said Rahman Aljebouri, a senior researcher at the National Endowment for Democracy.

“Both the United States and the factions that seek rapprochement will benefit from such a step. Washington, however, views the factions that have joined the political process and have a long political history to be the closest to it,” Aljebouri told Al-Monitor.

"The relations between the Badr Organization and the Americans have evolved through the ministries of Transport and Interior, which were [part of] Amiri’s party," he added.

Aljebouri’s suggestion that the United States deals with PMU factions separately is backed up by the US Congress’ stance on the League of the Righteous (Asaib Ahl al-Haq). Though Asaib Ahl al-Haq is part of the PMU, the United States has talked about placing Asaib Ahl al-Haq on its terrorism list.

The Fatah Alliance issued a calm and unprovocative statement June 2 calling on Washington to “reconsider the political map that will give it an appropriate opportunity to establish balanced relations with Iraq.”

Yehya al-Kubaisi, an adviser to the Iraqi Center for Strategic Studies, told Al-Monitor, “The United States cannot deal with the PMU as a single unit. They [Americans] have always distinguished between what they call good and bad militias. The Badr Organization is under the good category, while the League of the Righteous and Harakat Hezbollah al-Nujaba are categorized as bad. As for Iran, it believes that dealing with the former group of factions better serves its interests.”

He added, “The meeting between the US ambassador and Amiri happened at the same time the United States said it would classify the League of the Righteous and Harakat Hezbollah al-Nujaba as terrorist organizations. This means that Iran and the United States are sending each other messages, using the PMU as a tool to do so.”

As things stand, rapprochement between some PMU leaders and the United States stands to benefit both parties. The United States needs to neutralize Iran's role in these factions. The PMU, meanwhile, seeks to get rid of elements that might cause it to be categorized as a terrorist group or of having committed human rights violations.