*

Dollar index briefly hits lowest since late April and

recovers

*

US manufacturing contracts for third month

*

Euro dented by slower euro zone inflation

*

US job openings rebound in April; layoffs pick up

(Updates to U.S. morning)

By Saqib Iqbal Ahmed

NEW YORK, June 3 (Reuters) - The U.S. dollar rose on

Tuesday, pulling back from a six-week low against the euro, even

as investors remained concerned about potential economic damage

from the trade war waged by President Donald Trump's

administration.

"We had a big selloff in the dollar and we have it bouncing

back a bit today ... I don't think there has been a lot of fresh

news to say the dollar has turned in any kind of meaningful

way," said Marc Chandler, chief market strategist at Bannockburn

Global Forex LLC.

"I'd say the bounce is still fairly constrained, fairly

limited," he said.

The dollar was up 0.7% against the yen at 143.73.

The euro fell 0.5% to $1.1386, having briefly touched a

six-week high of $1.1454. Data earlier showed inflation in the

euro zone slowed below the European Central Bank's target of 2%,

underpinning expectations for a rate cut later this week.

For the year, the dollar is down about 9% against the euro.

While global equity markets have broadly recovered from an

early-April selloff in the wake of the on-again, off-again saga

of Trump's tariff threats, the greenback remains pressured.

U.S. duties on imported steel and aluminium are set to

double to 50% starting on Wednesday, the same day the Trump

administration expects countries to submit their best offers in

trade negotiations.

Trump and Chinese President Xi Jinping were likely to have a

call soon to iron out trade differences, Treasury Secretary

Scott Bessent said on Sunday, although on Monday there was an

angry rejection from China's Commerce Ministry of U.S.

accusations that Beijing violated their trade agreement.

"Trade developments remain crucial. Reports suggest China is

gaining leverage over the U.S. through its control of chip

supply chains and rare earths," ING strategist Francesco Pesole

said.

"Trump and Xi Jinping are set to speak this week, and past

direct talks have sometimes eased tensions. That leaves room for

a positive surprise that could help the dollar at some point

this week," he said.

On Tuesday, data showed U.S. job openings increased in

April, but layoffs picked up in a move consistent with a slowing

labor market amid a dimming economic outlook because of tariffs.

Fiscal worries have also given rise to a broad "sell

America" theme that has seen dollar assets from stocks to

Treasury bonds dropping in recent months.

Those concerns come into sharp focus this week as the Senate

starts considering the administration's tax cut and spending

bill, estimated to add $3.8 trillion to the federal government's

$36.2 trillion in debt over the next decade.

Still, traders in the foreign exchange options market are

positioned for the U.S. currency to weaken further.

The British pound was 0.3% lower at $1.35045 on Tuesday,

ahead of a raft of Bank of England speakers and an auction of

long-dated government bonds that may offer a gauge of investor

confidence in Britain's finances.

Bitcoin, the world's largest cryptocurrency by market

capitalisation, was 0.4% higher on the day at $105,364.