PHOENIX, United States, April 6 -- Though embroiled in conflicts and uncertainty across the Middle East, the United States still considers its strategic rebalance towards Asia and the Pacific crucial and will boost its security investment in the Asian-Pacific region, U.S. defense chief Ash Carter said Monday.

"Over the next decade, no region will matter more for American security and prosperity than the Asia Pacific," said Carter at Arizona State University's McCain Institute en route to Japan and South Korea in his first Asian trip. "I'm personally committed to overseeing the next phase of the rebalance, which will deepen and diversify our engagement in the region."

Carter made the remarks at a time when the U.S. military was again bogged down in the Middle East despite President Barack Obama's earlier pledge to end military involvement in the region.

In February, Obama submitted a war request to U.S. Congress, asking for force authorization against the extremist group the Islamic State against the will of his Democratic colleagues who were determined to prevent another ground assault similar to the Iraqi war. Republican hawks, though, regarded the Obama war request too weak.

In March, Obama promised the visiting Afghan President Ashraf Ghani not to cut the current 9,800 U.S. troops stationed in Afghanistan through 2015, though he had previously planned to reduce the current level to around 5,500 by the end of 2015 and withdraw all troops by the end of 2016.

Meanwhile, recent anarchy in Yemen, a predominant power base for the extremist group Al-Qaida in the Arabian Peninsula (AQAP), significantly damaged Washington's anti-terrorism strategy in the region.

"We will reinforce partnerships and alliance -- the bedrock of everything we do in the Asia Pacific," Carter said, in a bid to convince Americans, and most likely its allies in Asia its commitment to the "pivot to Asia" strategy put forward by the Obama administration in 2011.

Carter's upcoming trip to Asia is the first of the two scheduled in April and May. A U.S. Defense Department statement said earlier that Carter's April trip would focus on strengthening and modernizing America's alliances in Northeast Asia.

In Japan on April 8-9, Carter will meet with senior Japanese officials to discuss the defense strategic guidelines review ahead of Prime Minister Shinzo Abe's visit to Washington at the end of April, said the statement.

After his visit to Japan, Carter will visit Seoul, South Korea' s capital, on April 9-10, during which Carter will reiterate the U. S. commitment to South Korea's security and discuss regional issues with South Korean officials.

In May, Carter will also travel to Singapore and India with a focus on building and strengthening growing partnerships in South Asia and Southeast Asia, the statement said.

Carter will address the annual Shangri-La Dialogue security conference in Singapore, which the statement said he views as an important opportunity to engage with Singapore and other key partners in Southeast Asia.

During his visit to India, Carter will seek to strengthen U.S.- India defense cooperation, including the Defense Technology and Trade Initiative that Carter started when he served as deputy defense secretary, said the statement, adding that Carter also will engage India further on other Asia-Pacific issues.