MUMBAI, India -- President Obama opened his 10-day Asia trip on a somber note Saturday, memorializing the victims of the devastating terror attacks that tore through Mumbai two years ago. "We'll never forget," he said.

Obama spoke at the Taj Mahal hotel, a target of the 60-hour siege that killed 166 people across the city. The president said he intended to send a signal by making Mumbai the first stop on four-country Asia trip and by staying at the Taj.

"The United States and India stand united," he said.

The president spoke after meeting privately with relatives of those killed in the November 2008 attack. He and first lady Michelle Obama visited an outdoor memorial, an open-air fountain with floating flowers just off the lobby at the Taj.

He also signed a memorial book, writing, "The United States stands in solidarity with all of Mumbai and all of India in working to eradicate the scourge of terrorism."

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But illustrating the difficulties of the U.S.-India relationship even as Obama began a trip aimed at strengthening it, Indian commentators quickly seized on the president's failure in his spoken remarks to mention Pakistan. Pakistan was the home of the 10 assailants, the place where they trained and the base they used to launch the attack.

Pakistan is also India's archrival -- but a linchpin for Washington and its allies in the war in Afghanistan.

Obama said the U.S. and India are working together more closely than ever before to keep their people safe, describing the countries as "two partners that will never waver in our defense of our people."

Afterward, Obama visited a museum in a home where Mohandas Gandhi once lived. A framed illustration of Gandhi walking was at the center of the library in the steamy museum. The Obamas signed a guest book there, too. The president wrote that Gandhi "is a hero not just to India, but to the world" and his wife promised to "always treasure" the visit.

Obama also was set to address American and Indian business leaders and was expected to announce trade and export deals worth billions to the U.S. In the wake of the Democrats' devastating midterm election losses, attributed in part to the poor U.S. economy, the White House is intent on highlighting concrete benefits to U.S. consumers from Obama's foray overseas.

"It is hard to overstate the importance of Asia to our economic future," the president wrote Saturday in an op-ed in The New York Times.

The president left Washington shortly after the government reported that the economy added 151,000 jobs in October. It wasn't enough to lower a stubborn 9.6 percent jobless rate and the president said it wasn't good enough.

On the longest foreign trip of his presidency, Obama's business-first message is aimed particularly at India, where he is spending three full days. That's also the longest amount of time he has spent in any one country. The trip is also taking him to Indonesia, where he lived for four years as a youth, to South Korea for a meeting of the Group of 20 developed and developing nations, and then to Japan for an Asia-Pacific Economic Cooperation forum.

The White House is going to great lengths to bring attention to the economic potential and shared democratic values that define its relationship with India and its 1.2 billion residents.

Briefing reporters aboard Air Force One, National Security Adviser Tom Donilon said Obama intends the trip to be "a full embrace of India's rise."

"There's no more powerful way to do that than a presidential trip," Donilon said.

Indian officials said Obama's visit underscored the close ties that have developed between the two nations over the past 10 years after decades of wary relations.

"I don't think there's an area of human endeavor in which we do not actually cooperate," said Shivshankar Menon, India's national security adviser. "We work together in innovation. We work together in technology. We create jobs in each other's economy. When you look at the political military side as well, we work together on national security, on counterterrorism, defense."

But serious disagreements remain, and they appear unlikely to be resolved during Obama's visit.

India has raised concerns about the billions of dollars in military aid the U.S. is funneling to Pakistan. Indian leaders also are wary of comments by U.S. politicians against the outsourcing of jobs abroad, including to India.