Australian universities are “stagnating” under the weight of budget cuts to the sector, a major education ratings body has warned.

Six Australian universities have again been ranked in the top 100 in the world and nine in the top 200 on the 2019 Times Higher Education world university rankings, but the rankings agency warned the country’s universities were either treading water or going backwards because of cuts to the sector.

The University of Melbourne remained highest, staying at 32, followed by the Australian National University (49, down one), the University of Sydney (59, up two), the University of Queensland (69, down four), Monash (84, down four) and the University of New South Wales (96, down 11).

However, Ellie Bothwell, the global rankings editor at THE, said the picture in Australia was “a cause for concern”, as several universities recorded double-digit declines in their rankings.

“While there are some examples of progress from Australia this year, the national picture is a cause for concern, with many universities declining or remaining stagnant,” she said.

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“The country boasts some world-class institutions – and immense potential for greater success on the global stage.

“But you can’t sustain world-class universities and research facilities with funding cuts. To excel, universities need strong investment and they need to be able to attract and retain the very best global talent and research collaborations.

“As funding cuts take hold and pressure mounts to cap international student numbers – combined with intensifying competition from Asia – Australia’s universities could well face an uphill struggle in the coming years.”

The warning comes in the context of a period of enforced belt-tightening within the sector.

In December the federal government announced it would cut $2.2bn from universities predominantly through a two-year freeze in commonwealth grants funding.

While it did not directly cap student places, the decision effectively ended the previously bipartisan agreement on demand-driven funding because universities would no longer receive additional direct commonwealth grants funding if enrolments increased.

Universities have warned the cuts will unfairly affect regional universities and will mean that 9,500 fewer Australians can attend university in 2018, rising to 19,500 in 2019 and 23,000 in 2020.

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The government plans to introduce a performance-based funding mechanism in an attempt to address attrition rates and improve graduate outcomes.

The former education minister Simon Birmingham also argued the funding increase to universities since the introduction of demand-driven funding meant the sector has enjoyed “huge growth in university revenues and finances”.

However, the chief executive of Universities Australia, Catriona Jackson, said those comments “should prompt a government rethink and reversal of the funding cuts”.

“These ranking results confirm our world-class standing – but also show this is at risk unless those cuts are reversed,” she said. “We’ve been warning for some time about the damage of funding cuts on Australia’s rankings.”

Jackson said a decline in the quality of Australia’s universities would have a detrimental effect on the broader economy.

“Funding cuts are bad for local and international students. They threaten quality, [and] international education is built on quality,” she said.

“International students inject almost $32bn into Australia’s economy each year and support 130,000 Australian jobs. They also bring Australia and the world closer together, and build important diplomatic and personal ties.”

The ranking of New Zealand’s top university, the University of Auckland, also declined, falling out of the top 200.

Oxford University claimed first position for a third consecutive year, with Cambridge in second. Stanford in the US remained in third.