David Cameron and Barack Obama have issued a joint statement vowing to defeat "barbaric" radical Islamists and their "distorted ideology".
Writing for The Times (£), the world leaders together said: "Along with our French allies, we have made clear to those who think they can muzzle freedom of speech and expression with violence that our voices will only grow louder.
"Whether we are facing lone fanatics or terrorist organisations such as al-Qaeda, Islamic State (Isil) or Boko Haram we will not be cowed by extremists."
They also emphasised that the vast majority of Muslims are "sickened by the evil these terrorists claim to perpetrate in the name of Islam".
The statement comes in the wake of the murders of 17 people in Paris at the hands of extremists, as well as a barbaric Al-Qaida attack on a school in Pakistan and the use of schoolgirls as suicide bombers by African militant group Boko Haram.
The US is determined to help French authorities apprehend those responsible for the attack on the satirical newspaper Charlie Hebdo, President Barack Obama's spokesman has said.
Josh Earnest told CNN that US officials had been in close contact with their French counterparts and that they have been "stalwart allies" in the fight against Islamic State extremists.
"We know they are not going to be cowed by this terrible act," he added.
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A top al Qaida leader in Yemen has blamed US President Barack Obama for the recent deaths of two hostages during a failed rescue attempt.
Nasr bin Ali al Ansi's video message, obtained by Site Intelligence, is the first comment by al Qaida following the deaths of Luke Somers, a British born American, and South African Pierre Korkie.
Al Ansi said he warned the US against such attempts after a first failed rescue operation in November.
He accused Obama of showing carelessness for the life of an American citizen and claimed the raid "caused things to go in a completely different way than we wanted".
US President Barack Obama will welcome Prince William in the Oval Office during the Duke and Duchess of Cambridge's whistle-stop trip to America, the White House has announced.
The Duke is making a solo day visit to Washington DC to discuss the fight against illegal wildlife trafficking at the World Bank.
A spokesman said Mr Obama welcomed the Prince’s work in a "global fight" he described as "both a national security threat and a devastating environmental problem" and was keen to host him at the White House.
The President looks forward to thanking the Duke of Cambridge for the hospitality shown to him by the royal family during the President’s recent visits to the United Kingdom.
This visit underscores the special relationship between the United States and the United Kingdom.
Vice President Joe Biden will also host William for a separate meeting in the White House as the Duke makes his first visit to Washington, DC.
The pregnant Duchess will remain in New York for the duration of the three-day trip.
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President Barack Obama is "concerned and disappointed" at the violence that broke out after a grand jury decided not to indict the police officer who shot dead a black teenager in Ferguson, a White House spokesman said.
"We are all deeply worried and disappointed - and concerned about the violence, any sort of violence and that's why the President went out and spoke about it last night, spokesman Eric Schultz said.
"Again I would remind you the vast majority of protests in Missouri and around the country were peaceful and constructive".
Obama was delayed leaving the White House for Chicago in order to get a briefing about the situation in Ferguson from Attorney General Eric Holder, Schultz added.
US President Barack Obama has arrived in Australia to join other world leaders at the G20 summit in Brisbane.