US President Donald Trump greeted Japanese Emperor Akihito and Empress Michiko on Monday with a genteel handshake and nod, but no bow, avoiding the pitfall that led to criticism of his predecessor Barack Obama.

Mr Trump, wearing a suit and tie and his wife, Melania, in a long, dark blue dress, were met at the palace entrance by the royal couple, both wearing suits.

The President smiled, shook hands and nodded at the 83-year-old emperor before greeting the empress.

The four entered the palace where they chatted through interpreters in footage aired live on television, but without sound, as is customary.

After the meeting, the leaders shook hands again, and Mr Trump tapped the emperor’s arm repeatedly with his left hand.

“Thank you for the great meeting”, the President said to Akihito. “I‘m sure we will meet again”.

Bowing is considered an important symbol of respect in Japan.

But former US President Obama came under fire after meeting the emperor in Tokyo in 2009 for what critics back home said was bowing too low to Akihito. Some US commentators said the he should not lower his head before foreign monarchs.

Mr Obama also faced criticism from a different quarter - etiquette experts - who noted he combined a bow with a handshake, which is not traditionally done in Japan, whether meeting the emperor or anyone else.

President Obama bends low as he is greeted by Emperor Akihito and his wife Michiko (REUTERS)

Japanese guests are not supposed to touch the royal couple or shake hands, but foreign guests often do.

Hillary Clinton shook hands and air-kissed the empress on both cheeks, then took her hand as they entered the palace when she met the royal pair as Secretary of State in 2011, a month after the triple disasters of an earthquake, tsunami and nuclear meltdown hit north-eastern Japan in March of that year.

Akihito has spent much of his reign working to heal the wounds of the Second World War, which was waged across Asia in his father Emperor Hirohito's name.

Traditionalists say that Japan’s Chrysanthemum throne dates back more than 2,000 years. Akihito was the first royal heir in the Japanese imperial family to marry a commoner -- a symbol of Japan’s new modernity and confidence.

Japan earlier this year enacted a law clearing the way for Akihito to step down, the first abdication by a Japanese monarch in nearly two centuries. He will be succeeded by his son, Crown Prince Naruhito in late 2018 or early 2019.