LONDON (Reuters) - The euro inched slightly lower on Tuesday as the dollar gained some strength, though the pair remained close to an 11-week high as investors maintained their hope in a global economic recovery post coronavirus.

The optimistic mood persisted within markets despite growing concerns over U.S.-China tensions and mass protests across America over the death of a black man in police custody.

The euro was last trading hands at $1.1120, down 0.1% EUR=EBS, close to March 17 $1.1154 high it rose to on Monday. The U.S. dollar fell to a three-month low of 1.3530 against the Canadian dollar and was last trading down 0.2% CAD=D3.

The safe-haven Japanese yen fell 0.2% versus the greenback to 109.79 JPY=EBS.

The U.S. dollar index against a basket of six major currencies =USD fell to its weakest level since mid-March, at 97.73, before settling in neutral territory at 97.82.

The index has fallen about 5% from a peak hit in March when panic over the COVID-19 pandemic gripped the world’s financial markets, prompting investors to scramble for the safety of dollar cash.

“The strengthening of the commodity-linked currencies and the weakening of the safe havens suggest that investors’ appetite remained supported for another day,” said Charalambos Pissouros, Senior Market Analyst at broker JFD Group.

“It seems that investors continued placing bets on the prospect of a global economic recovery as governments around the globe continue to ease their lockdown measures,” Pissouros said.

Market risk sentiment was hurt only slightly on Monday when Bloomberg reported China had told state-owned firms to halt purchases of soybeans and pork from the United States, raising concerns that the trade deal between the world’s two biggest economies could be in jeopardy.

Investors’ economic optimism has so far also survived the rising social unrest in the United States where President Donald Trump vowed to deploy thousands of heavily armed soldiers and law enforcement to halt violence in the U.S. capital and other cities if mayors and governors failed to regain control of the streets.

The protests erupted over the death of George Floyd, a 46-year-old African-American who died in Minneapolis police custody after being pinned beneath a white officer’s knee for nearly nine minutes.

Elsewhere, the pound rose to a one-month high of $1.2554 GBP=D3 after news emerged that Britain may indicate its willingness to compromise on fisheries and trade rules if the European Union agrees to back off from its "maximalist" demands related to regulatory alignment and fishing access.

The UK and the EU walk into a new round of talks this week ahead of the June 18-19 summit by which Britain is expected to say whether it requires an extension to the December deadline of the transition period.

Sterling was last down 0.3% at $1.2533.