Central banks worldwide have joined together to declare that they stand in "full solidarity" with the Federal Reserve chair after the US launched a criminal investigation into Jerome Powell.

The heads of the Bank of England, the European Central Bank and the Bank of Canada are among 11 senior bankers who have signed a statement highlighting the importance of independence in setting interest rates.

"Chair Powell has served with integrity, focused on his mandate and an unwavering commitment to the public interest," they said.

The Department of Justice is conducting the probe. President Donald Trump has said he did not "know anything" about the investigation.

The probe is linked to testimony Powell gave to a Senate committee about renovations to Federal Reserve buildings.

It follows a year of relentless attacks on the Fed chair by Trump, who has pushed the Fed to lower borrowing costs more aggressively.

As well as criticising Powell's decisions on interest rates, Trump has made personal comments, calling the Fed chair a "major loser" and a "numbskull".

Commenting on the Fed chair, the global central bankers said in their joint statement: "To us, he is a respected colleague who is held in the highest regard by all who have worked with him."

Until the weekend, Powell had stayed largely silent in the face of Trump's attacks but on Sunday, he publicly pushed back and warned that the independence of the US central bank was at stake.

"This is about whether the Fed will be able to continue to set interest rates based on evidence and economic conditions, or whether instead monetary policy will be directed by political pressure or intimidation," Powell said.

The Fed has cut interest rates three times since September, leaving its key lending rate at around 3.6%.

But policymakers are divided about what to do next. Some are worried additional reductions could stoke inflation, which continues to bubble.

Consumer prices rose 2.7% over the 12 months to December, according to official figures published on Tuesday. That was the same rate as in November and remained higher than the Fed's 2% target.

In their joint statement on Tuesday, the international financial institutions said: "The independence of central banks is a cornerstone of price, financial and economic stability in the interest of the citizens that we serve.

"It is therefore critical to preserve that independence, with full respect for the rule of law and democratic accountability."

Powell, who Trump nominated as Fed chair in 2017 during his first term in the White House, is set to step down in May.

Trump is expected to name his successor in the coming weeks.

Several Republicans have spoken out against the justice department's move against the Fed.

North Carolina Senator Thom Tillis, a Republican who is a member of the Senate Banking Committee, said he would oppose the nomination of Powell's replacement by Trump, and any other Fed Board nominee, until the matter was "fully resolved".

The committee must approve the next Fed nominee so if Tillis keeps that pledge, it could delay the nomination of any Trump pick to replace Powell.

His Republican colleague on the committee, Senator Kevin Cramer, said he thought Powell was a poor Fed chairman but did not believe he was a criminal. To restore confidence in the Fed, he added, the investigation should be swift.

Another Republican senator, Lisa Murkowski, described the investigation as "an attempt at coercion".

Powell has also been backed by three former chairs of the Fed - Janet Yellen, Ben Bernanke and Alan Greenspan. A number of other eminent former officials have publicly declared their support for him and the bank's independence.

Yellen, who was Powell's immediate predecessor, said the criminal investigation was "extremely chilling", adding that investors should be concerned.

"You have a president that says the Fed should be cutting rates to lower rate payments on the federal debt… It is the road to banana republic," she told CNBC.

The signatories in full are:

• Andrew Bailey, governor of the Bank of England
• Christine Lagarde, president of the European Central Bank
• Erik Thedéen, governor of Sveriges Riksbank
• Christian Kettel Thomsen, chairman of the Danmarks Nationalbank
• Martin Schlegel, chairman of the Swiss National Bank
• Michele Bullock, governor of the Reserve Bank of Australia
• Tiff Macklem, governor of the Bank of Canada
• Chang Yong Rhee, governor of the Bank of Korea
• Gabriel Galípolo, governor of the Banco Central do Brasil
• François Villeroy de Galhau, chair of the Bank for International Settlements
• Pablo Hernández de Cos, general manager of the Bank for International Settlements