President Barack Obama has said the relationship between the US and the UK is "special" and "stronger than it has ever been".
At a joint press conference in London with David Cameron, Mr Obama said the two men "saw eye to eye" on a range of issues.
Mr Cameron hailed the relationship as "essential for our security and prosperity".
Both men reiterated their calls for Libyan leader Col Gaddafi to step down.
The two men earlier held talks in No 10, which were expected to focus on the conflicts in Libya and Afghanistan.
Mr Cameron said they had discussed a range of subjects, including recent developments in the Middle East, including in Syria and Yemen, the fight against terrorism and the need to create jobs in the global economy.
'Shared ideals'
He said he had come to know the President well over the past year and had come to "value his leadership and courage".
He described UK-US relations as "a living, working partnership" which were "essential to our security and to our prosperity".
But he refused to be drawn on comparisons between the two men's relationship and that between President George W Bush and Tony Blair, saying each personal relationship between world leaders was different.
President Obama, who will later make a key foreign policy speech to MPs and peers on the second day of his state visit, said the US-UK relationship was based on "shared ideals and shared values" not merely "warm sentiment and common history".
"It is a special relationship and an essential relationship. I believe it's stronger than it has ever been and I'm committed to making sure that it stays that way," he said.
On Libya, Mr Cameron said there was no future for the country with Col Gaddafi in power and both the UK and US were looking at "all options" for "turning up the heat" on the regime.
Mr Obama said the international community had made "enormous progress" in Libya in saving civilian lives.
"Gaddafi and his regime need to understand there will be no let-up in the pressure we are applying," he said, adding that the US was "strongly committed to seeing the job through".
President Obama said he believed Nato forces were "turning the corner" in Afghanistan while Mr Cameron urged the Taliban to make a "decisive split" with al-Qaeda if they wanted to participate in a political dialogue and bring about stability.
Debt issues
More widely, Mr Cameron said the international community needed to seize the "once in a generation moment" to support pro-democracy movements in the Middle East.
He said he would push for a "major programme" of political and economic support for reformist governments in the region at the G8 later this week. President Obama condemned regimes using violence against their people.
Asked about the two governments' approaches to economic recovery and deficit reduction, Mr Cameron said both countries were committed to reducing debt levels over the next few years.
President Obama said that although the pace at which they did this would differ, both shared the same goal of creating "broad-based prosperity" but also ensuring governments "lived within their means" and "never mortgaged our futures".
Later in the day, Mr Obama will give a setpiece speech on US foreign policy at Westminster Hall - the oldest building within the Palace of Westminster - an honour usually reserved for British monarchs.
