The site crashed around 3 p.m. Saturday. It coincided with midnight celebrations in Japan when revellers were sending a record 16,197 tweets per second, the Daily Mail reported Sunday.
The overload meant no one could post new messages or read existing ones. Instead, frustrated users were greeted with the error message: 'Twitter is over capacity.'
The site returned to working order but then stopped on several other occasions, prompting speculation that it was being hit by the arrival of New Year in different parts of the world.
The meltdown happened as the world welcomed in 2012, a year of historic importance for Britain, with the Olympics, the Paralympics and the Queen's Diamond Jubilee set to be defining moments.
Up to 250,000 people poured into Central London, some in Trafalgar Square and others watching the pyrotechnics centred on the London Eye, the Mail said.
In Tokyo, people released helium balloons in front of the Tokyo Tower at midnight with notes attached listing their hopes for 2012. Many wished for a better year, following the earthquake and tsunami of 2011, the newspaper added.