PASpeaking at the G20 summit in Turkey, the PM said Friday's attacks in Paris "underlined the threat we all face".World leaders have agreed to do more to share intelligence and cut off funding for terrorists, David Cameron has said.
Earlier he met Russia's President Vladimir Putin to discuss tackling the Islamic State group and the Syrian war.
He said the gap between Russia and the West's position on Syria "has been enormous", but now "everyone recognises the need for compromise".
Multiple attacks on bars, restaurants, a concert hall and the Stade de France on Friday left 129 people dead, including Briton Nick Alexander from Essex. IS leaders have claimed the group was behind the killings.
French PM Manuel Valls said the attacks were organised from Syria, and warned authorities believe new attacks are being planned in France and other European countries.
It comes as a total of 23 people have been arrested and weapons seized in raids on suspected Islamist militants across France.
In the UK, a minute's silence for the victims was held at 11:00 GMT, to coincide with a Europe-wide silence at midday French time.
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Speaking at a press conference at the G20, Mr Cameron said there would "need to be compromise on both sides" between the West and Russia in order to find a political solution in Syria.
Russia began carrying out air strikes in Syria in support of President Bashar al-Assad in September, saying it was targeting IS.
However, there have been suggestions from Syrian opposition and others that non-IS rebels are bearing the brunt of Russian attacks.
"I've said Assad should go immediately, and we have to compromise and recognise there is going to have to be a transition," Mr Cameron said.
But he maintained "the fact that Assad can't play a role in the long-term government of Syria is not a political preference, but a political fact."
Analysis
PABy BBC diplomatic correspondent James Robbins
Both the British and Russian sides emerged from these talks sounding conciliatory and positive, stressing the importance of working together to end the war in Syria as a key element in the fight against extremism.
David Cameron told President Putin that Russian bombing of the moderate opposition in Syria was a "mistake", but after the talks Mr Cameron said there were signs that the Russians were focusing more on IS targets.
The prime minister also said the gap between those who believed Syria's President Assad must go immediately, and President Putin who continued to support him, was reducing.
Mr Cameron said it would need compromise on both sides to close the gap further and faster. The hope is that prospects for a UN supervised peace process are improving, although substantial obstacles do remain.
Mr Cameron also said people should be "vigilant" against those who want to "change our way of life and destroy our way of life", and called for Britain to show "resolve" and "carry on with our lives".
The terror threat level in the UK has been at "severe", meaning an attack is highly likely, since last August.
In other developments:
- Number 10 says UK security services have disrupted seven attacks this year, including one in the last month
- The Foreign Office is advising people travelling to France to exercise caution in public places and follow advice of local authorities
- The government has announced funding to allow MI5, MI6 and GCHQ to recruit an extra 1,900 officers - a 15% increase
- A doubling in funding for aviation security is also expected. The UK currently spends about £9m a year on this issue
- Labour leader Jeremy Corbyn says renewed air strikes by French forces targeting IS militants will "probably not" make a difference
- The UK is to co-host a donors' conference in London next year to raise "significant new funding" to address the Syrian crisis
- All 23 France players will travel to England on Monday after turning down the option to withdraw from Tuesday's friendly football match at Wembley
- John Sawers, former head of MI6, writing in the Financial Times, said "political calculation and available operatives" will determine IS's next target
- Global concert firm Live Nation said it would be increasing security at its venues
Civil war erupted in Syria four years ago, and now President Bashar al-Assad's government, IS, an array of Syrian rebels and Kurdish fighters all hold territory. Millions have been displaced and more than 250,000 people killed as a result of the fighting.
French aircraft bombed Raqqa, the stronghold of IS in Syria, following Friday's attacks.
Syria vote
Mr Cameron has reiterated that he will not ask Parliament to vote on extending British military action into Syria until there is enough support.
"I need to build the argument, I need to take it to Parliament, I need to convince more people," he said.
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Former defence secretary Liam Fox said the UK's failure to bomb IS targets in Syria was damaging its global reputation.
But he said bombing had limitations and "we're not going to be able to destroy ISIS [Islamic State] purely from the air - it is going to require co-ordination on the ground at some point".
Seven attackers died in the assault on the French capital, most of them after detonating suicide belts. Five were identified over the weekend, and on Monday another two were named.
Meanwhile in the UK, officers from the Met Police's Counter Terrorism Command unit are interviewing people returning from France who may have information.
The Met is also appealing for any potential witnesses to contact its anti-terrorist hotline, on 0800 789 321.
