David Cameron should abandon his “contradictory war aims” and accept that President Bashar al-Assad must remain in power to allow his army to take the lead in defeating Islamic State forces in Syria, former chief of the defence staff Gen David Richards has said.

As the prime minister prepares the ground for a Commons vote on extending RAF airstrikes against Isis forces from Iraq to Syria, Lord Richards called for Britain and other allied nations to broker a deal with Russia that would pave the way for Assad’s forces to lead the charge against Isis on the ground.

In an interview on BBC Radio 4’s Today programme on Wednesday, he said: “At the moment we’ve got contradictory war aims. We want to deal with Isis but we also want to get rid of Assad at the same time. I personally don’t think that’s plausible. Any general will tell you you need to have unity of purpose and clear aims in a war. That muddies those aims.”

The prime minister, who had insisted that Assad must be removed from power as a first step to building a new settlement in Syria, has softened his language in recent weeks as he seeks to win Russian support for targeting Isis. He has spoken of how Assad could remain in power for a transitional period as part of an overall political settlement in Syria.

But Richards called for Cameron to go further and to accept that Assad’s army and his Hezbollah and Iranian backers are the only credible force that could fight Isis on the ground in Syria.

He said: “The real issue is can you use the one army that’s reasonably competent which is President Assad’s army? In that respect I personally would see a ceasefire being agreed in the way people are now talking, allowing potentially Assad’s army and Hezbollah and their Iranian backers and others to turn their attention on Isis in a sequential operation. After that the politics would kick in and you would have to do something about the residual political structure within Syria.”

Richards said a failure to use Assad’s forces would risk a repeat of the chaos in Iraq in the wake of the 2003 invasion. “Do we want to invite chaos by forcing [Assad] out without some sort of successor government that will ensure order at least in their own areas? In the areas controlled by Assad it is a functioning government. The dustbins are emptied. We don’t want to see what happened in Iraq in 2004/05/06 where it was chaotic because we couldn’t manage the aftermath. We have to be very careful that we don’t wish for something we don’t want. As much as we have awful dislike and distaste for Assad I would like to see him kept with his government in place at least for a while.”

Richards also pointed out that Britain and its allies, who have agreed “deconfliction measures” with Russia to ensure their aircraft avoid each other in the skies over Syria, have said a deal would have to be brokered with Moscow. He said: “Russia is, whether we like it or not, a leading part of this. Along with the very sad events in France you could say it was their intervention that has catalysed this change of thinking. We have just got to accept the reality that they are there.”

The intervention by Richards, who has a habit of speaking his mind, came after Cameron said it was his “firm conviction” that Britain should extend its airstrikes against Islamic State targets from Iraq to Syria. The prime minister told parliament that the Paris attacks had shown the UK faced a “direct and growing” threat. He announced plans to set out a “comprehensive strategy” on Syria towards the end of next week in an attempt to get a Commons majority before Christmas to approve airstrikes in the country. A vote will only be held if the strategy is well received.

Reporting back after the G20 summit in Turkey, Cameron told MPs: “My firm conviction is that we need to act against [Isis] in Syria. There is a compelling case for doing so.”

The announcement marked a change of tack by Cameron, who had indicated as recently as Monday that he was wary of tabling a vote on the grounds that a failure to win MPs’ support would damage the UK. Theresa May, the home secretary, also said on Monday that the prime minister would come back to the Commons on Syria “only when there is a consensus”. The Guardian, Times (paywall) and FT reported this month that he had decided to shelve a vote because Russia’s military intervention in Syria had complicated the situation and he had failed to win over enough Labour MPs to neutralise a Tory rebellion.

But Cameron indicated that the scale of the attacks in Paris and the cross-border planning by Isis had convinced him that Britain should join the coalition led by the US and France in hitting Isis targets in Syria.