Story highlights "It looks beautiful," President Obama says about National September 11 Memorial

Obama signs a steel beam to be placed at the top of the tower

It is Obama's fourth visit to the site

One World Trade Center is expected to be completed next year or in early 2014

With the under-construction One World Trade Center fast approaching its final height, President Barack Obama visited the New York tower Thursday to get an update on its growth and help prepare one of the finishing touches.

"It looks beautiful," the president said to first lady Michelle Obama as they stood at a window on the 22nd floor and looked down on the National September 11 Memorial and Museum being built below.

Obama flew into New York's John F. Kennedy International Airport in the late afternoon and traveled by motorcade to the construction site for a briefing on the building, currently 104 stories and 1,300 feet tall -- already the tallest structure in New York.

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He was joined by New York Gov. Andrew Cuomo, New Jersey Gov. Chris Christie and New York Mayor Michael Bloomberg.

Obama also visited with workers representing over 60 labor unions working on the site as he signed one of the final steel beams to be installed as part of the building's framework at the top of the tower.

"We couldn't be prouder of you guys," Obama told them. "This is what the American spirit is all about."

According to reporters at the scene, Obama wrote on the steel beam: "We remember we rebuild we come back stronger! Barack Obama "

The visit to the Lower Manhattan site is Obama's fourth. He last visited it in September to mark the 10-year anniversary of the 2001 attacks by al Qaeda that killed more than 2,000 people and destroyed the twin towers of the World Trade Center.

Under construction since 2006, One World Trade Center surpassed the Empire State Building (1,250 feet) as the city's tallest structure in April. The tower's builders say it will surpass Chicago's Willis Tower as the tallest building in the United States, with a final height of 1,776 feet -- a nod to the year of the Declaration of Independence.

One World Trade Center is expected to be completed next year or in early 2014.

Obama's visit was the first of his three New York stops on Thursday. He'll attend two fundraisers in the evening -- including one at the residence of actress Sarah Jessica Parker -- before he returns to Washington late Thursday night.