David and Samantha Cameron laid flowers at the World Trade Centre memorial on Thursday as they paid their respects to the victims of 9/11.
The prime minister and his wife, Samantha, bowed their heads in silence beside the reflecting pool which acts as a memorial site on the footprint of the former North Tower of the World Trade Centre.
Cameron played down the significance of a Taliban threat to break off talks on a political settlement in reaction to the massacre of 16 Afghan citizens by a renegade US soldier.
"I think we just have to be clear that we have a plan in Afghanistan, which is to hand over to a capable Afghan army, police and government at the end of 2014," he said.
"We will do that without a political settlement or with a political settlement. That is up to the Taliban.
"Every time they appear on the battlefield they lose, and lose decisively. Their ranks of commanders have been massively depleted.
"They have the choice - a political settlement where they give up weapons and become part of Afghanistan's political future or they take this attitude and Afghanistan will take care of its own security."
Reflecting on the decade which followed 9/11, the prime minister said: "Of course we have made big sacrifices - and Britain in particular losing over 400 of our soldiers - but I do think it is worth remembering that almost 3,000 people died here in New York, including 67 British citizens.
"The plots then were all coming from Afghanistan and Pakistan. And whereas a few years ago about 90% of the plots we were disrupting on the streets of London and New York and elsewhere were coming from the Pakistan/Afghanistan area, that is now maybe half that figure.
"So we have made progress in making our world safer, but it is very hard, very difficult work."
Mrs Cameron laid a posy of white roses on the spot where the name of British victim Katherine Wolf is engraved alongside nearly 3,000 others who lost their lives.
The prime minister said the visit brought home to him forcefully the reasons why British troops are fighting in Afghanistan.
"Here at the site of the Twin Towers, Ground Zero, here is the place to remember why what we do overseas is so important, so people are safe at home," he said in a round of TV interviews.
For the Camerons, the visit to Ground Zero was particularly emotional, as Samantha - then pregnant with their first child - was in New York on the day of the 9/11 attacks and her husband spent several anxious hours trying to reach her by mobile phone.
In his previous job as an executive for Carlton TV, Mr Cameron attended meetings in the Twin Towers.
The couple met Charles Wolf, whose wife Katherine died aged 40 on 9/11. Originally from Swansea, Mrs Wolf moved to the US after meeting her American husband and had been working with Marsh & McLennan in the North Tower for just three weeks before the attacks.
After meeting the Camerons, Mr Wolf said: "It's a great honour. It was very, very nice for both he and his wife to come. It was very personal as well as being official.
"Of course they have had their own loss of their child, and when you are with someone who's had a recent loss like that, you know you are with people who get it, who care."
Before going to pay their respects, the couple went up into one of the new skyscrapers being built around the Ground Zero site, where Port Authority officials showed them plans for the redevelopment of the area.
The Camerons took a constructors' lift up the outside of One World Trade Centre to the 21st storey of the half-built tower, which will be New York's tallest building when it is completed - standing higher than the Twin Towers at 1,776ft (541m).Suggest a correction