Iraqi government forces and Kurdish peshmerga fighters have launched attacks to recapture two towns in the north from Islamic State (Isis) militants, as Western governments consider how to mount an effective response to the threat posed by the extremist group that has redrawn the border of Iraq and Syria.

The Kurdish forces, backed by US air power, took one district near the eastern entrance to Jalawla, 70 miles (115km) north-east of Baghdad. Jalawla was taken by Isis more than a week ago. Iraqi troops supported by Iraqi fighter planes were advancing towards the nearby town of Saadiya. Both towns are near the Iranian border and the semi-autonomous Kurdish region.

Shirko Mirwais, an official from the Patriotic Union of Kurdistan (PUK) party, said the battle to reclaim Jalawla had already left several dead on both sides. "The peshmerga advanced on Jalawla from several directions" before dawn, he said, adding that they had already taken back several positions, cutting off the militants.

He said nine peshmerga had been wounded in the fighting but could not say how many had been killed. Another PUK official, Mullah Bakhtiar, confirmed the operation was under way and said it had already achieved some of its goals.

Kurdish forces lost at least 10 fighters when Isis took Jalawla, one of the deadliest flashpoints along the peshmerga's 600-mile (1,000km) front.

In Syria, government forces have sent reinforcements to an airbase under attack by Isis militants, the last government foothold in north-east Syria, an area largely controlled by jihadi fighters. The Syrian Observatory for Human Rights, a group monitoring violence in Syria, said the reinforcements had been flown in overnight to Tabqa, 25 miles (40km) east of the Isis stronghold of Raqqa.

The group said about 30 Isis fighters had been killed and dozens more wounded on Thursday by heavy bombardment and landmines in areas surrounding the base. Boosted by US weapons seized in Iraq, Isis has taken three Syrian military bases in the area in recent weeks.

Since 8 August, nearly two-thirds of the 90 US strikes have taken place near the critical Mosul dam, which Barack Obama this week declared was no longer under Isis control.

Amid the latest fighting, Britain's former head of the army, Lord Dannatt, said the west must build bridges with Bashar al-Assad, the Syrian president, to tackle Isis. Speaking on the BBC Radio 4 Today programme, Dannatt said the group had to be "opposed, confronted and defeated" in both Iraq and Syria.

"The Syrian dimension has got to be addressed. You cannot deal with half a problem," he said. "The old saying 'my enemy's enemy is my friend' has begun to have some resonance with our relationship with Iran. I think it's going to have to have some resonance with our relationship with Assad."

Dannatt continued: "I think whether it is above the counter or below the counter, a conversation has got to be held with him. Because if there are going to be any question of air strikes over Syrian airspace it has got to be with the Assad regime's approval."

The former army chief said he believed more UK special forces might need to be deployed on the ground in Iraq to train Kurdish troops in how to use weapons. He also suggested the "time will come" when the government decides that British planes should carry out air strikes, rather than leaving it to the US.

But American and British officials have firmly ruled out co-operation with Assad. Philip Hammond, the British foreign secretary, said he did not believe an alliance with the Assad regime would not be "practical, sensible or helpful".

Asked if the UK would have to collaborate with the Assad regime, Mr Hammond told BBC Radio 4's World at One: "No. We may very well find that we are fighting, on some occasions, the same people that he is but that doesn't make us his ally."

Although US officials have described Isis as an "apocalyptic" organisation that poses an "imminent threat", the highest ranking officer in the American military said that in the short term, it was sufficient for the US to "contain" the group, which has taken over large chunks of territory in Syria and Iraq.

Army general Martin Dempsey, chairman of the joint chiefs of staff, said on Thursday that cross-border action was necessary to defeat the group. He played down, however, speculation that US warplanes would strike Isis in Syria as well as Iraq.

Isis "will have to be addressed on both sides of what is at this point essentially a non-existent border", he said, which would require "a variety of instruments, only one small part of which is air strikes. I'm not predicting those will occur in Syria, at least not by the United States of America."

Ben Rhodes, a deputy national security adviser and one of Obama's most trusted foreign policy aides, told a radio interviewer that allying with Assad and his "barbarism" - a word US officials also use to describe Isis - is off the table.

"We basically think that the reason that Isil was able to get the safe haven that they have established in parts of Syria is because of Assad's policies. His barbarism against his own people created an enormous vacuum. ... He's part of the problem, Assad," Rhodes told National Public Radio on Thursday, using the US government's preferred acronym for Isis.

From the Obama administration's perspective, a viable strategy against Isis hinges on cleaving Sunnis on both sides of the border - "the 20 million disenfranchised Sunnis that happen to reside between Damascus and Baghdad," as Dempsey put it on Thursday. Backing Assad, their enemy, forecloses on that option, the thinking goes.

At the Pentagon, defence secretary Chuck Hagel called Assad "probably the central core" of US woes in the region.