Britain will not work with Syrian President Bashar al-Assad in the battle against Islamic State (IS) extremists, the foreign secretary has told the BBC.
Philip Hammond said to do so would not be "practical, sensible or helpful".
Former head of the Army Lord Dannatt and ex-Foreign Secretary Sir Malcolm Rifkind called for the move following the beheading of US journalist James Foley by IS militants.
Mr Hammond also defended the monitoring of suspected extremists in the UK.
The UK government has called for President Assad to be removed as Syrian leader as a result of his actions during the country's civil war.
Speaking on BBC Radio 4's The World at One, the foreign secretary said to co-operate with the Syrian regime would "poison" what the UK was trying to achieve.
He said: "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."
Earlier, Lord Dannatt called for a dialogue.
He told BBC Radio 4's Today programme: "I think whether it's above the counter or below the counter, a conversation has got to be held with him."
Sir Malcolm, the chairman of Parliament's Intelligence and Security Committee, said history had shown that "sometimes you actually have to make an arrangement with some nasty people in order to get rid of some even nastier ones".
The US has described IS, which has seized large swathes of northern Iraq, as the biggest threat it has faced in recent years.
In the video of Mr Foley's murder, IS militants threatened to kill another American if the US did not stop its air strikes against the group in northern Iraq.
Police and security services are trying to identify the jihadist - who had an English accent - who appeared in footage of Mr Foley's killing.
Unconfirmed reports suggest the man is from London or south-east England.
Mr Hammond said the authorities were "devoting significant amounts of resource to identifying the individual".
The government has defended its approach to extremists at home, following calls for a change in strategy prompted by the killing.
Mr Hammond said "significant powers" were available to deal with people planning to travel to Syria or Iraq to fight including withdrawing passports, monitoring them while overseas and arresting them on their return.
The Independent Reviewer of Terrorism Legislation, David Anderson, said the right balance had been achieved between protecting freedom and security.
However, Mr Anderson said he had recommended tougher restrictions on terror suspects kept under Terrorism Prevention and Investigation Measures (TPims).
TPims are used to restrict movement, the use of computers and mobile phones and meetings with others. They replaced the previous system of control orders - which were more restrictive - in 2011.
Lord Carlile, a former independent reviewer of terrorism laws, said no TPims were currently in place, because ones previously imposed had all expired.
He said: "The government decided to have no more, for reasons which I have never understood."
He called for control orders to be reintroduced and for more investment in the Prevent strategy, which distributes money to anti-extremism schemes across the country.
He added: "We must ensure that the Prevent strand of counter-terrorism policy is given the funding it needs so that it can work in all parts of the country".
The Home Office said TPims had been introduced because control orders were not working and were being "struck down by the courts".
It said the "strongest possible action" would be taken to protect national security, adding: "Ultimately the best place for terrorists is behind bars and we will prosecute those who break the law."
Usman Nawaz, a former government adviser on extremism, told the BBC: "I don't think the government is doing enough to have a conversation with young Muslims, or to understand what's going on in the mind of young Muslims, the vast majority of whom completely reject the ideas and ideologies of [IS]."
A former Labour Foreign Office minister, Kim Howells, said successive governments and religious leaders were to blame for the radicalisation of Muslims in Britain.
Mr Howells said it was time to address the "narrative" among some Muslims that they were the victims of a "plot" to suppress them.