David Cameron has said he wants to see peaceful transition of power in Syria, rather than revolution, ahead of talks with US President Barack Obama.
The UK prime minister said he was frustrated at the "appalling" situation in Homs, which has been under assault by government forces.
Mr Cameron also said the public wanted "an endgame" to the war in Afghanistan.
The leaders are expected to agree that Afghan forces should take over a lead combat role early - by mid-2013.
However, Mr Obama has said there will be no "rush for the exits". British and US combat troops are expected to leave Afghanistan by the end of 2014.
The first day of Mr Cameron's three-day visit saw the leaders emphasise the importance of the "special relationship" between the two nations.
And Mr Obama made Mr Cameron the first foreign leader he has welcomed onto the presidential plane Air Force One, as they travelled to Ohio to watch a university basketball game.
Shared foreign policy concerns, such as the situations in Iran and Syria, are also expected to be high on Wednesday's agenda.
The leaders will discuss diplomatic and economic measures to increase pressure on the Syrian regime of President Bashar al-Assad.
And Mr Cameron told reporters in Washington: "We're all frustrated by Syria. What's happening in Homs is completely appalling."
The United Nations has suggested more than 8,000 people have died since anti-government protests erupted a year ago, with many casualties in Homs where government forces have been trying to root out rebel fighters.
"I'm endlessly kicking the tyres and asking what else can be done," said Mr Cameron.
"The shortest way of ending the violence is a transition where Assad goes, rather than a revolution from the bottom. Transition at the top rather than revolution at the bottom."
'No terror haven'
However, the conflict in Afghanistan is expected to dominate Wednesday's talks.
The visit comes at a tense time for Afghanistan after an American soldier shot dead 16 Afghan civilians. As an Afghan government delegation visited the site in Kandahar on Tuesday, they came under attack from militants.
Mr Cameron acknowledged the country would not have a "perfect democracy" by 2014. But he envisaged "leaving Afghanistan looking after its own security, not being a haven for terror, without the involvement of foreign troops".
Downing Street would not confirm a detailed timetable for the handover of combat duties to Afghan troops, but the BBC understands an agreement will be made to hand over the lead combat role in 2013.
The White House talks will be followed by a press conference and lunch attended by UK Chancellor George Osborne, Foreign Secretary William Hague, US Vice-President Joe Biden and Secretary of State Hillary Clinton.
Together with wife Samantha, Mr Cameron is later expected to visit a school for children with disabilities. A state dinner will round off the day.
The guest list includes UK stars including Homeland actor Damian Lewis and Northern Irish golfer Rory McIlroy, with entertainment provided by British folk group Mumford and Sons and US R&B star John Legend.
Mr Cameron made his first official visit to the US as prime minister in July 2010. The latest meeting comes ahead of Nato and G8 summits.