Volodymyr Zelenskyy promised a new bill to strengthen the rule of law in Ukraine on Wednesday, in an apparent attempt to assuage popular anger at his decision to weaken the powers of two independent anti-corruption agencies.

Thousands of protesters took to the streets of Kyiv for a second day, while European leaders expressed concern at the Ukrainian president’s contentious decision. The demonstrators gathered outside the presidential office, shouting anti-government slogans.

They want him to scrap a controversial law that effectively places the agencies under government control. In a video address, Zelenskyy sought to deflect criticism by promising a new presidential bill.

It would guarantee the independence of anti-corruption institutions and at the same time ensure there was “no Russian influence”, he said. “Of course, everyone has heard what people are saying these days – on social media, to each other, on the streets. It’s not falling on deaf ears,” he added.

But the apparent concession left protesters unimpressed. They said Zelenskyy has not agreed to scrap the controversial aspects of Tuesday’s bill and pointed out that the Verkhovna Rada – Ukraine’s parliament, which approved the changes – has gone on holiday for the summer recess.

Olha Ivanova, who has worked in the anti-corruption sector, said the government was calculating that the protests would fizzle out. She predicted they would continue. “Civil society is huge in Ukraine. From time to time we have to remind the people in power that we elect them,” she said.

Ivanova held up a placard in English and Ukrainian that read: “Have you lost your mind?” She said she hoped Zelenskyy would reverse his decision, adding: “He’s not a dictator. Nobody would say this. He’s a president in a very difficult political context during a war.”

Ukraine’s European backers including Germany, France and Sweden have echoed concerns about the new legislation, which the Ukrainian president approved on Tuesday night. They warned it could hamper Kyiv’s attempt to join the EU and hinder the fight against corruption.

The bill gives sweeping powers to the prosecutor general’s office. It can now decide which cases the two independent agencies – the national anti-corruption bureau and the specialised anti-corruption prosecutor’s office – are allowed to pursue.

The two institutions have been key to fighting high-level corruption and protecting billions in international aid and investment. Critics say they have been stripped of their autonomy, making them indistinguishable from ordinary law enforcement bodies.

Zelenskyy says the shake-up was needed to clean Ukraine’s “anti-corruption infrastructure” of alleged Russian connections. On Wednesday, he convened a meeting with the heads of law enforcement and anti-corruption agencies at his presidential office in Kyiv.

Olena Kurnytska, a 21-year-old student at York University, took part in Wednesday’s protest for the first time. She waved a placard saying “I would like to see the future, not the flashbacks”. She said: “We feel like its our civic duty to be here. It’s an easy situation to exploit. A wartime government can twist democracy more easily.”

Ursula von der Leyen, the head of the European Commission, was one of several prominent European figures who voiced unhappiness at the legislative amendments. She had asked Zelenskyy for explanations and had conveyed to him her strong concerns, her spokesperson said.

They added: “The respect for the rule of law and the fight against corruption are core elements of the European Union. As a candidate country, Ukraine is expected to uphold these standards fully. There cannot be a compromise.”

In a pointed message to Kyiv, the EU’s defence commissioner, Andrius Kubilius, said trust during wartime was “easy to lose with one significant mistake by the leadership … Transparency and open European dialogue is the only way to repair [it].”

France’s European minister, Benjamin Haddad, said there was still time for Ukraine to reverse its decision. “It is not too late to go back on this,” he told France Inter radio. “We will be extremely vigilant on the subject.”

The popular backlash against the bill is turning into the biggest domestic political crisis of Zelenskyy’s premiership. The crowd on Wednesday was larger than the night before. The street protests, which took place in several cities, were the first since Vladimir Putin’s 2022 full-scale invasion.

Civil-society leaders have accused the presidential administration of violating an informal contract with society. They say the agreement with government – that it was inappropriate to criticise official abuses because of the war with Russia – is definitively over.

About 3,000 demonstrators gathered directly outside Zelenskyy’s administration complex on Wednesday evening, shouting slogans beneath his window. They included “shame”, “we are the power”, and “veto the law”.

Posting earlier on Telegram, Zelenskyy said Ukrainians faced a “common enemy” in the shape of “Russian occupiers”. Of public criticism, he said: “We all hear what society says. We see what people expect from state institutions to ensure justice and the efficiency of each institution.”

Yuriy Sak, a former adviser to Ukraine’s defence ministry, said Ukrainians had a strong historical tradition of protesting against anything that resembled authoritarianism or dictatorship, in Soviet times and today.

“It’s in our DNA. We have a very good sense for where the red line is, and for when people cross this line. If anyone tries to tighten their grip on power people pour into the streets,” he said, citing the uprisings in 2004 and 2014 against perceived government misrule.

Sak likened the collective mood to the air raid alerts that sound most evenings, when Kyiv and other cities came under Russian missile attack. “Whenever we see authoritarianism on the move, a silent siren goes off in Ukrainian heads,” he suggested.