By Hannah Lang and Yadarisa Shabong

(Reuters) - The U.S. dollar staged a tentative rebound against its major peers on Wednesday on hopes of de-escalating trade tensions and as President Donald Trump backed away from threats to fire the head of the Federal Reserve, offering relief to investors.

The Wall Street Journal also reported on Wednesday that the White House was considering slashing China tariffs in an effort to de-escalate the trade war between the two countries, boosting the greenback against the euro and the Swiss franc.

Markets this week have been grappling with the notion that the Fed's independence could be under threat after repeated verbal attacks by Trump on Chair Jerome Powell for not cutting rates since the president took office in January.

Trump appeared to back down in remarks late on Tuesday.

"I have no intention of firing him," Trump told reporters in the Oval Office. "I would like to see him be a little more active in terms of his idea to lower interest rates."

Lee Hardman, senior currency analyst at MUFG, said the "outright denial" from Trump was an encouraging signal for the markets.

Trump and U.S. Treasury Secretary Scott Bessent separately suggested that there could be a de-escalation in U.S.-China trade tensions and any trade deal with China could "substantially" cut tariffs.

Investors hastened back to the dollar, which has been hovering near three-year lows in recent weeks and whose safe-haven status had been questioned in view of Trump's trade policies and their potential impact on the U.S. economy.

The U.S. dollar index rose rapidly at the start of the trading day in Asian hours, but steadied since then as market sentiment remained fragile. It was last down 0.106% at 99.46.

The euro eased 0.51% to $1.1362, pulling back from the $1.15 levels it saw earlier this week that marked a roughly 3-1/2-year high.

Surveys on Wednesday showed euro zone business growth stalling and Germany's private sector contracting this month, hurt by service sector woes and trade-related uncertainty. 

"The uncertainty and anxiety emanating from the US appears to be impacting growth in Europe more quickly and aggressively than expected," said Kyle Chapman, FX markets analyst at Ballinger Group, in a research note.

'MARKETS DON'T TRUST' TRUMP

The dollar climbed more than 1% against the yen to 143.21 in early trading and was last up 0.53% at 142.37. Against the Swiss franc, the dollar was last 0.84% stronger at 0.8257, having jumped more than 1% earlier in the Asian session.

Despite its attempted rebound, the dollar is not far off its multi-year lows against the euro and the Swiss franc and seven-month low versus the Japanese yen. 

"We think this is going to be a theme going forward. We will see continued shocks that place downside pressure on the dollar, repeated walk backs to see the dollar bounce. But again, the dollar will not return to previous highs," said Nicholas Rees, Head of Macro Research at Monex Europe. "Markets don't trust Donald Trump." 

Beyond Trump's attacks on the Fed, investor focus has been on potential trade deals between the U.S. and other countries. 

After setting a baseline import tax of 10% and much higher on dozens of countries at the start of the month, Trump abruptly put the steeper levies on hold for 90 days for countries to negotiate less stringent rates.

White House press secretary Karoline Leavitt said on Tuesday that 18 countries have offered proposals so far, with Trump's trade negotiating team set to meet with 34 this week to discuss tariffs.

In cryptocurrencies, bitcoin rose over 2% to $93,168, breaking above $90,000 for the first time since March.

(Reporting by Hannah Lang in New York; Additional reporting by Ankur Banerjee in Singapore; Editing by Kim Coghill, Hugh Lawson, Chizu Nomiyama and Frances Kerry)