The Obamas welcomed at Buckingham Palace

In lavish style, President Barack Obama and Queen Elizabeth II on Tuesday affirmed a bond between the United States and the United Kingdom that has strengthened through the sacrifice of war and a history of common values. As the queen put it, the relationship is "tried, tested and, yes, special."

For his part, the president, dressed in white-tie tuxedo for a glitzy dinner at Buckingham Palace, said in a toast that the relationship "never rests."

"We can have confidence in the partnership that our two countries share, based on the rock-solid foundation built during Queen Elizabeth's lifetime of extraordinary service to the nation and to the world," the president said at a dinner in which White House staffers mixed with U.S. movie stars and British royalty.

Obama immersed himself in grandeur Tuesday as the queen welcomed him to Buckingham Palace for the first day of a state visit that kept the president largely out of sight for most of the British public.

There was an elaborate arrival ceremony on the steps of the palace's West Terrace, complete with a 41-gun salute; a tour of the Queen's private gallery, where the monarch highlighted items she thought would hold personal significance to the president; and a short meeting with newlyweds Prince William and Kate Middleton.

But the pomp and pageantry happened largely behind the palace walls. Though pictures of Obama's visit blanketed British television, the president made no formal remarks Wednesday, except for a brief statement on the deadly tornadoes in the U.S.

The day stood in stark contrast to Obama's stopover Monday in Ireland, where the U.S. president with a touch of Irish in his family history set out to connect with the public. And the Irish returned the embrace, often literally, lining the streets of Moneygall, the tiny village that was home to Obama's great-great-great grandfather, and packing central Dublin for the president's speech on the deep bonds between the U.S. and Ireland.

Here in London, small crowds gathered outside of Buckingham Palace and Westminster Abbey, where the president laid a wreath at the tomb of the unknown warrior. But the best they could hope for was a quick wave from the president as he entered his limousine or a glimpse of him as his motorcade sped by.

Obama did break away from the formality of the royal family for a trip to a local school, where he and British Prime Minister David Cameron visited a science class and played table tennis with students.

Obama and Cameron will hold substantial meetings Wednesday on Afghanistan, Libya and counter-terrorism, and the president will address the British parliament, delivering a speech that aides say will offer reassurances that the U.S. still values its traditional allies in Europe.

Before delving back into heavy foreign policy matters, the Obamas will be guests of the queen at a lavish banquet at Buckingham Palace Tuesday night. About 170 members of the royal family and other dignitaries are expected to attend.

Obama is only the second U.S. president to be accorded a state visit in Britain during the reign of Queen Elizabeth II, according to Buckingham Palace. Although most previous presidents have visited England and met the queen, a number of features are required by British protocol in order for the trip to be considered a state visit. George W. Bush is the only previous U.S. president to be accorded a state visit, according to Buckingham Palace.

The queen is said to be quite fond of the Obamas, having first met them in London in 2009. A palace official said the she was closely involved and interested in the planning of this state visit, a grand event that only happens about twice a year for a world leader of the queen's choosing.

The president and first lady Michelle Obama had plenty of quality time with the queen Tuesday, including when she gave them a post-lunch tour of the Buckingham Palace art collection, pointing out various items as the president and first lady looked on with interest.

The president stopped in front of a page from King George III's personal journal, dated sometime around 1783, not long after America won its independence. "America is lost!" the king had written, before meditating on the possibilities of "a future friendship and connection."

Obama also looked at a photograph of the HMS Resolute, the ship whose timbers were used in the 19th century to build a desk presented by Queen Victoria to America. The desk has been used by most presidents since then, including Obama, in the Oval Office. "That's my desk!" the president could be heard to exclaim.

As is customary, there was an exchange of gifts: From the Obamas to the queen, a collection of memorabilia and photographs from her parents' 1939 visit to the United States, and from the queen to the Obamas a selection of letters from the royal archives to and from past U.S. presidents and English monarchs. The Obamas struck a highly personal note with their gift for the queen, who is said to have been very close to her parents.

The president also paid a visit to Westminster Abbey where he laid a wreath at the Grave of the Unknown Warrior. But the president suffered a momentary lapse, pausing to ask for spelling help as he wrote a message in the abbey's distinguished visitors' book. Then he dated his note May 24, 2008. He wasn't even president then.