Prime Minister David Cameron and US President Barack Obama have vowed a united front against the threat posed by Islamist extremists and their "distorted ideology."

In a joint opinion article that appeared in Times, Cameron and Obama outlined the principles of the US-British alliance ahead of two days of White House meetings.

The two leaders are to have a working dinner on Thursday night and hold more talks on Friday.

Obama and Cameron, noting the Paris attacks last week against a satirical newspaper, said extremists would not muzzle freedom of speech.

"Whether we are facing lone fanatics or terrorist organisations such as al-Qaeda, Islamic State or Boko Haram, we will not be cowed by extremists. We will defeat these barbaric killers and their distorted ideology," the leaders wrote.

Obama and Cameron were also firm in their resolve to stand up against Russia's aggression in Ukraine. They pledged to maintain diplomatic pressure on Moscow.

The United States and Europe have imposed a variety of sanctions against Russia in retaliation.

"If we allow such fundamental breaches of international law to go unchecked, we will all suffer from the instability that would follow. Our strong and united response has sent an unmistakable message that the international community will not stand by as Russia attempts to destabilise Ukraine," they wrote.