Barack Obama on Saturday strutted the stage of William Shakespeare's Globe Theatre in London, joining in festivities to mark 400 years since The Bard's death.

The US president was treated to scenes from Hamlet on his early morning visit to the Globe Theatre, a reconstruction on the banks of the River Thames of a theatre dating back to the 16th century.

Actors from a company that embarked a two-year world tour in 2014, playing to more than 100,000 people in 197 countries, put on a special performance for the president.

Obama stood in the open-air theatre watching intently, swaying back and forth on his feet to the music.

He clapped loudly following the show and joined actors on the stage afterwards.

"Let me shake hands with everyone. That was wonderful. I don't want it to stop," Obama said.

He was also given a tour of the playhouse by Patrick Spottiswoode, director of Globe Education.

"You're doing a great job," he told Spottiswoode.

The Globe was rebuilt close to its original site and stages authentic period performances of plays by Shakespeare and others.

William Shakespeare's hometown of Stratford-upon-Avon on Saturday leads the global celebrations to mark four centuries since his death, with star-studded plays, concerts and parades.

Focal points for the celebrations include Shakespeare's family home in Stratford, where it is assumed he was born in 1564, and the Holy Trinity Church, where he was buried.

From Warsaw, to Dubai and Las Vegas, Shakespeare's plays will also be playing to packed houses to mark the occasion, highlighting the international appeal of the English language's leading playwright.