Thousands of Hungarians have marched across central Budapest in a show of support for the European Union, protesting against what a new political movement sees as a creeping rise in Russian influence under prime minister Viktor Orbán.

The rally follows a series of major demonstrations in Budapest in recent weeks, triggered by a new law that would drive out of Hungary a top university founded by US financier George Soros.

Momentum, an upstart political movement that called for Monday’s rally dubbed “We belong to Europe,” announced it would run at a parliamentary election next April.

“Healthcare, education, [public] transportation are failing,” András Fekete-Győr, the Momentum leader, told demonstrators. “We struggle to make things work every day.”

Fekete-Győr added that the group would unveil its election manifesto in October.

The group gained national prominence with a referendum campaign that torpedoed Orbán’s bid for Budapest to host the 2024 Summer Olympics.

Orbán, a former critic of Moscow, changed tack after returning to power in a 2010 landslide. In a key speech, he called for transforming Hungary into an “illiberal state,” citing Russia and Turkey as templates for success.

He still holds a firm lead in opinion polls. But on Saturday he told leaders of his centre-right EU political group he would comply with demands from Brussels to change measures branded an attack on academic freedom.

“Viktor Orbán’s performance at the European parliament has shown that it is not only Hungarians who are tired of Orbán and his Fidesz party,” said Daniel Kiss, a 23-year-old university student, who carried EU flags at the rally with his girlfriend.

Hungarians attend a pro-European Union rally in Budapest. Photograph: Bernadett Szabo/Reuters

“He blasts the EU, but at the same time we need European money to stay afloat,” he said. “We have had enough.”

Orbán has said Hungary should remain a member of the EU, but is also seeking reforms and wants to avoid a further loss of national sovereignty.

In the past seven years, Orbán has eliminated checks on his power by taking control of the public media, curbing the powers of the constitutional court, and placing loyalists in top positions at public institutions.

But Orbán’s unorthodox fiscal stabilisation measures have slashed the budget deficit, sent unemployment to record lows and Budapest forecasts economic growth above 4% this year and next, which would be the fastest rates since Orbán took power.

Despite the street protests, the fragmented Hungarian opposition so far looks unable to mount a serious challenge.

A survey in April by thinktank Zavecz Research put support for Orbán’s Fidesz party at 27% of voters. The Socialist party scored 13%, the nationalist Jobbik 11% and Momentum just 2%.

Even some protesters, like 26-year-old Bence, who wore a mask of Vladimir Putin on the back of his head, were sceptical of a breakthrough next April.

“In such an election system, even Momentum or some other smaller opposition party getting into parliament would be a big deal,” he said. “But that is just what this is all about.”

