The Chinese mainland now hosts the two best universities in Asia, according to the latest edition of the Times Higher Education World University Rankings.

The report shows Peking University has overtaken the National University of Singapore to take second position among Asian institutions, and Tsinghua University is the first.

The Chinese mainland also has the most universities in the top 200 listing from among Asian economies, with seven making the list.

The two best Asian universities, Tsinghua University and Peking University, are in 23rd and 24th position, respectively, on the global stage.

Some Chinese mainland institutions saw their rankings slip, with Nanjing University falling 10 places to joint 144th, and Zhejiang University falling six places to joint 107th.

But,overall, the picture is one of continued progress.

Shanghai Jiao Tong University leapfrogged numerous United States and United Kingdom institutions to rise 32 places, to joint 157th, driven mainly by a significant increase in its research environment and its industry income score.

Globally, the Chinese mainland is in joint sixth place in terms of the number of universities it has in the top 200 – tied with Canada and Switzerland, demonstrating that while it has succeeded in getting more institutions onto the list, it has not yet broken the Anglo-American dominance at the highest level.

Outside the Chinese mainland, Hong Kong continues to perform well, given its size, with five institutions making the global top 200, of which three are in the top 60.

The University of Hong Kong still leads the charge, in 35th place, one higher than last year. It is the only Hong Kong university in the top 200 to have improved its position on last year. The region's four other institutions in the top 200 each fell, by between four and 16 places.

The National Taiwan University is the only institution from Taiwan to have made the top 200, rising 50 places to joint 120th. The strong performance was primarily due to improved citation scores.

Phil Baty, Times Higher Education chief knowledge officer, said: "It has long been clear that the emerging countries of Asia are going to play an increasingly powerful role among the global elite of higher education. It must also be stated, however, that the traditional Anglo-American powerhouses will not be displaced at the top of our rankings with ease."

Ellie Bothwell, Times Higher Education rankings editor, said: "The most noteworthy development in Asia over the past 12 months is that mainland China is now home to the top two universities in the continent for the first time, after taking the number one spot last year – a remarkable achievement."

British and US universities have continued to dominate the upper echelons of this year's rankings. The University of Oxford once again tops the table, with its rival UK institution, the University of Cambridge, dropping to third place behind the California Institute of Technology. Stanford and the Massachusetts Institute of Technology round out the top five.

The US is home to 60 of the world's top 200 universities, with 10 of them from the state of California. US institutions did see a slight drop in their average ranking overall, although among countries with more than 50 entrants, US universities are still ranked highest on average.

Europe makes a strong showing once again, with almost half of the global top 200 coming from the continent.

Baty said: "Future editions of the World University Rankings will most likely reveal intense competition, and while European and American institutions face significant hurdles, Chinese and other Asian universities have challenges of their own they must meet. These include ensuring that the excellent academics they produce do not move abroad to more established institutions in Europe and North America, promoting a culture of scholarly creativity and freedom, and boosting ties with nations across the globe."