Iran’s military has said it has targeted the headquarters of Iranian Kurdish forces in northern Iraq, stepping up strikes on Kurdish regions in both Iran and Iraq.

The military said it attacked “Kurdish groups opposed to the [Islamic] revolution in Iraqi Kurdistan with three missiles”. One person was killed and three injured in the strikes on Tuesday and Wednesday, the BBC has confirmed.

Tehran is intensifying its attacks on Iranian Kurdish groups in Iraq amid reports that US President Donald Trump wants them to join the fight against Iran as US and Israeli strikes continue.

Kurdish Iranian opposition parties in Iraq have denied reports that some of their forces have crossed into Iran.

“This is not true. Do not believe it,” said Hanna Hussein Yazdan Pana of the Kurdistan Freedom Party (PAK). “Not a single Peshmerga [fighter] has moved. No one moves alone.”

She said six Kurdish opposition groups – which recently formed a coalition – were coordinating their plans but needed the Americans to pave the way for a move. She told the BBC nothing would happen this week.

“It’s not about the hours or days. We cannot move if the air above us is not cleaned. We need to see weapons depots [of Iran’s security forces] being destroyed. Otherwise, it would be suicidal.”

Pana also called for a no-fly zone to protect Kurdish forces.

“The regime is very brutal,” she said, “and the most advanced weapon we have is a Kalashnikov.”

Kurdish soldiers joining the war

There has been growing speculation the Trump wants Kurdish forces to join the war to provide boots on the ground.

The White House has denied a report that the president is considering arming them.

Sir Simon Gass, a former British ambassador in Tehran, described Iran as “a patchwork of different ethnicities” with a Persian majority and significant minorities of Kurds, Balochs, Arabs and Azeris.

“If the United States and Israel find a way to ignite some of those groups into armed insurrection against the regime, it will be another problem which the regime needs to manage. It will be extremely difficult,” he told BBC Radio 4’s Today programme.

Gass said Iranian Kurdish opposition fighters were “relatively lightly armed”, and “under normal circumstances you would not expect them to be able to stand up to the strength of the Iranian armed forces.”

“However, if they are supported by special forces from other countries who can call in air support – that could be a different matter,” the former diplomat added.

More than 30 million Kurds inhabit a mountainous region straddling the borders of Turkey, Iraq, Syria, Iran and Armenia. They make up the fourth-largest ethnic group in the Middle East, but they have never obtained a permanent nation-state.

About 10% of Shia Muslim-majority Iran’s 91 million population are Kurds, who are mainly Sunni Muslims and live mostly in the country’s northwestern regions.

Amnesty International has said that Iranian Kurds have “long suffered deep-rooted discrimination” and that “their social, political and cultural rights have been repressed, as have their economic aspirations”.