US President Barack Obama has met the exiled Tibetan spiritual leader, the Dalai Lama, at the White House despite warnings by China that this would damage the bilateral diplomatic relations.

The closed-door meeting on Wednesday came at a time of heightened tensions between the US and China over Beijing's assertive pursuit of territorial claims in East Asia.

Obama's fourth White House meeting with the Dalai Lama in the past eight years took place in the White House residence, instead of the Oval Office where the president normally meets world leaders.

White House spokesman Josh Earnest said the choice of the residence emphasised the "personal nature of their meeting".

READ MORE: Obama's Dalai Lama greeting criticised by China

He said Obama had thanked the Dalai Lama for his condolences for the victims of Sunday's mass shooting at a gay club in Orlando, Florida.

Earnest added that Obama had in the past spoken of his "warm personal feelings" for the Dalai Lama, appreciation of his teachings, and belief "in preserving Tibet's unique religious, cultural and linguistic traditions".

At the same time, Earnest said the US position of considering Tibet part of China had not changed.

Warning from Beijing

China's foreign ministry said earlier it had lodged diplomatic representations with the US over the planned meeting, saying it would damage Chinese-US ties.

Ministry spokesman Lu Kang said the meeting would encourage "separatist forces", urging Washington to cease any support for Tibetan independence.

China considers the Dalai Lama a dangerous separatist.

The Dalai Lama, who fled Tibet into exile in India in 1959 after a failed uprising against Chinese rule, says he wants genuine autonomy for Tibet, not independence.

On Wednesday, a Chinese observation ship shadowed a US aircraft carrier in the Western Pacific, the carrier's commander said, as it joined warships from Japan and India for drills close to waters Beijing considers its backyard.

Japan and the US worry that China is extending its influence into the Western Pacific with submarines and surface vessels as it pushes territorial claims in the neighbouring South China Sea.

China has been angered by what it views as provocative US military patrols close to the islands. The US says the patrols are to protect freedom of navigation.