Thousands took to the streets across Ukraine this week to protest against legal changes that removed the independence of key anti-graft agencies, NABU and SAPO.

They were the country's first large-scale demonstrations since Russia invaded more than three years ago.

The changes also raised concerns in the European Union, a key ally to Ukraine in its war against Russia, which has said reforms are essential for closer European integration.

"Bill 13533, submitted by the President of Ukraine as urgent, restores all procedural powers and guarantees of independence of the NABU and SAPO," NABU said in a statement.

Both agencies took part in the preparation of the new draft law, it added.

Zelensky had promised on Wednesday he would propose a new bill on anti-graft agencies to parliament just a day after having approved the controversial reforms.

The European Union welcomed his new position.

On Thursday, Zelensky wrote on social media that he had just approved the text of the new bill.

"It is important that we respect the position of all Ukrainians and are grateful to everyone who stands with Ukraine," he added.

Zelensky also discussed the issue with the British and German leaders.

He invited Berlin to join "the expert review of the bill" and Britain's Prime Minister Keir Starmer suggested involving experts in scrutinizing it, Zelensky said in a statement after phone calls with the leaders.

Zelensky's deputy prime minister in charge of Ukraine's EU integration, Taras Kachka, reassured the bloc's ambassadors that the independence of anti-corruption bodies remained a "priority".

But a solution that would satisfy all parties was needed, he added.

The earlier version of the bill that was aimed at curbing independence of anti-graft bodies was swiftly approved by the parliament on Tuesday and signed by Zelensky into law on the same day.

It was aimed at placing the National Anti-Corruption Bureau of Ukraine (NABU) and Specialised Anti-Corruption Prosecutor's Office (SAPO) under the direct authority of the prosecutor general, who is appointed by the president.