The ship, which is called the Carl Vinson, will dock off Danang, which is the main Vietnam port that has been the landing area for American ships for many years.
China lays claim to nearly the entire energy-rich and strategically-important South China Sea, but several other nations such as Malaysia, Brunei, the Philippines, Taiwan and Vietnam have overlapping claims.
"They understand well the strategic rationale behind the rapprochement between Vietnam and the US, which was largely driven by China's growing assertiveness in the South China Sea", he said.
Economic relations with the United States in recent years have served as a counterbalance to Vietnam's political affinity with China.
The Vietnamese leader was quoted by the Asian Age; "We reaffirm our close collaboration to support India to further its relations and multi-faceted connectivity with ASEAN attaching high importance to the maintenance of security, maritime safety and freedom of navigation and over flight, settlement of disputes by peaceful means on the basis of worldwide law". "I am confident that engagements like this will further expand the comprehensive partnership between the United States and Vietnam".
The nuclear-powered Vinson carries 5,500 crew and up to 90 aircraft.
The warship is anchored just two nautical miles off Danang, a port city with high historical significance where American troops first landed for war.
San Diego-Based USS Carl Vinson Making Historic Port Call in Vietnam
The visit of an aircraft carrier - a more than 100,000-ton manifestation of US global military projection - reaffirms closer relations as Beijing flexes it political, economic and military muscle in Southeast Asia, and Washington seeks to re-establish its influence. It's been a routine deployment and everything we've seen has been exceptionally professional'.
Although there was no formal defense treaty signed, both leaders emphasized that ensuring a stable rule based order and freedom of navigation in the Indo-Pacific was essential for the peace and prosperity of the region.
The nuclear-powered USS Carl Vinson is home to 5,300 sailors, pilots and crew and 72 aircraft and will be in Danang - once a key US airbase - until its departure on Friday. Taiwan, Malaysia and Brunei also have claims.
Since 2014, China has forged ahead with island-building in the disputed waters, despite a landmark ruling in 2016 by the Permanent Court of Arbitration in The Hague, which said there was no legal basis for China's maritime claims.
"The Philippines has just rolled over, China is continually militarizing and if the United States doesn't maintain a presence in the region, Vietnam's got nowhere to hide", Thayer said.
Yet it is far from assured if the highly symbolic USS Carl Vinson's high-profile visit will soon translate into a tangible military alliance against China. The 1,000 foot-long (300 meter) ship weighing 95,000 tons will be in Danang until its departure on Friday.
Navy musicians from the US 7th Fleet Band will perform free concerts for the public as well.
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