Both the US and the UK have one fewer institution in the top 500 this year, but there was a better performance by some North American and European countries and little evidence of more Asian representation in the Academic Ranking of World Universities 2013.
In the top 10, positions were largely unchanged, with Harvard University topping the table, the University of Cambridge coming fifth, and the University of Oxford 10th.
There are now no Asian universities in the top 20 after the University of Tokyo was displaced by the Swiss Federal Institute of Technology Zurich at number 20.
China (which has 28 in the top 500), Taiwan (9), Hong Kong (5), Singapore (2), India (1) and Malaysia (1) all have the same number of universities in the table as last year.
South Korea (11) had one more institution than in 2012, but Japan (20) has one fewer.
Meanwhile, Canada (23), Germany (38) and Portugal (4) all grew their tally by one each.
There continues to be just a single country representative of Asia in the top 100 – Japan.
However, the University of California, Berkeley, rose from fourth to third, swapping places with the Massachusetts Institute of Technology.
The UK now has 37 universities in the top 500 after Swansea University dropped off the list. It has nine universities in the top 100, the same as last year, with University College London and Imperial College London remaining in 21st and 24th place respectively.
Lower down the table, some UK universities managed to improve their positions: the University of Bristol jumped six places to 64th; King’s College London moved up one to 67th; and the University of Nottingham rose three places to 83rd. The US has 149 universities in the top 500, and 52 in the top 100, one fewer than last year.
For the first time the King Abdullah University of Science and Technology, founded in Saudi Arabia in 2009 with a $10 billion (£6.5 billion) endowment, has entered the table.
However, in the 401-500 sector of the list, it still has a long way to go to realise its ambition of being among the top 10 science and technology institutions by 2020.
The table is based on six, largely research-based, measures. It comes ahead of the launch of the Times Higher Education World University Rankings, which will be unveiled at the THE World Academic Summit on 3 October in Singapore.