Kurdish Iranian dissidents in northern Iraq told The Associated Press that they are not preparing an imminent cross-border operation into Iran, even as they acknowledged they could join a future U.S. ground invasion. The comments were delivered by officials associated with the Kurdistan Freedom Party PAK, as Iraqi Kurdish authorities work to prevent any use of their territory as a starting point for attacks that could widen the war sparked by U.S. and Israel’s strikes on Iran.

In an interview Thursday, Khalil Nadiri, an official with PAK, said the dissident group is not planning an attack “but would join a ground invasion if the U.S. were to launch one,” according to his remarks reported by AP. Nadiri said the message was aimed at reassuring Iraqi Kurdish officials who have expressed concern they would be further dragged into the fighting from within Iraq’s semiautonomous Kurdish region.

Nadiri said that in the event of a U.S. ground operation, “then we would enter alongside the coalition forces,” and he added, “The Kurds must not place themselves as the spearhead of the attack.” He also said his group has armed members already present inside Iran and that it would not necessarily rely on cross-border support to stage an uprising.

Nadiri said Kurdish groups have been in contact with the U.S. and Israel, but he denied that they have received material aid from them. His comments came after Kurdish officials said earlier in the week that Kurdish Iranian dissident groups based in northern Iraq were preparing for a potential cross-border military operation in Iran, and that the U.S. had asked Iraqi Kurds to support them.

Rebaz Sharifi, described by AP as a military commander with PAK, characterized U.S. arming of the Kurdish dissidents as “a very positive development,” while still denying that the group has received such support so far. Sharifi said he expects that at some point U.S. President Donald Trump “might want the peshmerga forces of Eastern Kurdistan to participate in the conflict during a ground invasion,” and he said, “if it reaches that point, we, for our part, would be pleased with it.”

At the same time, Sharifi said both he and Nadiri sought to dispel fears among Iraqi Kurdish officials that the region could become a launching pad for operations into Iran. In a statement earlier this week, Peshawa Hawramani, a spokesperson for the Kurdistan Regional Government, said allegations that the region is part of a plan to arm and send Kurdish opposition parties into Iranian territory were “completely unfounded,” and he said the Iraqi Kurdish parties do not want to “expand the war and tensions in the region.”

AP reported that Iran and allied Iraqi militias have launched dozens of missiles and drone attacks into northern Iraq, including strikes targeting U.S. bases and the U.S. consulate in Irbil, as well as bases associated with the Kurdish dissident groups. Sharifi said PAK’s bases have been attacked twice with ballistic missiles and four times with drones since the start of the war, killing one fighter and wounding three others.

Nadiri linked his group’s restraint to Iraqi Kurdish policy, saying that because the Kurdistan region adopted a policy of not becoming “a part of this conflict” and because the dissidents “respect the laws of this region,” “the environment has not yet been established for us to move our forces back into Eastern Kurdistan.” He said the term “Eastern Kurdistan” is the one used by Kurdish groups to refer to the Kurdish region of Iran.

The prospect of Kurdish involvement also raised tensions with other Iranian opposition groups, AP reported, including a faction led by Reza Pahlavi that has accused the Kurdish dissidents of separatism and trying to carve up Iran. Sharifi said PAK’s “ultimate goal is the statehood of the Kurds in all four regions and the reunification of Kurdistan,” referring to Kurdish areas currently split among Iran, Iraq, Turkey and Syria. Nadiri said a confederal system could be “a viable solution” that would allow the Kurdish area to remain part of Iran while maintaining its “own sovereignty, identity, and unique characteristics.”