The Iraqi prime minister, Nouri al-Maliki, said on Thursday that he welcomed a Syrian air strike on Sunni militant positions as it left both countries "winners".

The Syrian warplanes struck near the border crossing in the town of Qaim on Tuesday, hitting the Islamic State in Iraq and the Levant (Isis), which seeks to carve out a purist Islamic enclave across the Syria-Iraq border.

Details are, however, sketchy. The White House spokesman Joshua Earnest earlier said Washington had "no reason to dispute" reports that Syria had struck within Iraqi territory but Maliki told the BBC that Bashar Assad's airforce had stuck to its side of the border.

"There was no coordination involved, but we welcome this action. We welcome any Syrian strike against Isis, because this group targets both Iraq and Syria ... But we didn't make any request from Syria. They carry out their strikes and we carry out ours. The final winners are our two countries," he said in an interview with BBC Arabic.

An initial translation supplied by the BBC said Maliki had confirmed Syrian airstrikes in Iraq but this was later corrected to Syria.

Syria's state news agency also denied that Damascus had carried out attacks in Iraq. It said its source "refuted allegations made by malicious media outlets who claimed that the Syrian air force shelled areas within the borders of Iraq".

Syrian opposition activists have meanwhile claimed that the Qaim strikes missed Isis's main bases and killed 30 civilians. Sabah Karkhout, head of Iraq's Anbar provincial council, told CNN that Tuesday's air attacks had hit inside Iraq in Rutba, al-Walid and Al-Qaim.

The raid, which puts Assad and Maliki in alignment against a common enemy, comes as Iran and the US are intensifying their presence in Iraq. 300 US military advisers arrived in Baghdad this week and surveillance drones are flying over northern Iraq. US officials said Iran was also flying drones in the country, controlling them from an airfield in Baghdad. The officials said they believed the drones were surveillance aircraft only, but could not rule out that they may be armed.

A senior Iraqi intelligence official said Iran was secretly supplying the Iraqi security forces with weapons, including rockets, heavy machine guns and multiple rocket launchers. "Iraq is in a grave crisis and the sword is on its neck, so is it even conceivable that we turn down the hand outstretched to us?" said the official.

The intelligence-gathering and arms supplies come on the heels of a visit to Baghdad this month by one of Iran's most powerful generals, Qassem Soleimani, commander of the Revolutionary Guard's Quds Force, to bolster the defences of the Iraqi military and the Shia militias that he has armed and trained.

The involvement of Syria and Iran in Iraq suggests a growing cooperation among the three Shia-led governments in response to the raging Sunni insurgency.

The US secretary of state, John Kerry, on Wednesday warned of the dangers of the Isis insurgency spreading into a larger conflict. "We've made it clear to everyone in the region that we don't need anything to take place that might exacerbate the sectarian divisions that are already at a heightened level of tension," he told a meeting of Nato foreign ministers in Brussels. "It's already important that nothing take place that contributes to the extremism or could act as a flash point with respect to the sectarian divide."