The dollar fell modestly against the Japanese yen on Tuesday, suggesting investors were skeptical of the optimism expressed by President Donald Trump on the possibility of a U.S.-Chinese trade deal days after the two countries raised tariffs against each other.

On Friday, China said it would increase tariffs on $75 billion worth of American goods. The United States retaliated by saying it would raise existing tariffs on $250 billion worth of Chinese goods to 30% from 25% on Oct. 1.

On Monday, speaking on the sidelines of the G7 summit of world leaders in France, Trump said Chinese officials had contacted U.S. trade counterparts overnight and offered to return to the negotiating table. Trump's comments sparked a wave of so-called risk-on trades, which initially boosted the dollar, weakened safe-haven currencies, and lifted stock markets.

However, doubts crept in after a Chinese Foreign Ministry spokesman said he was unaware that a phone call had taken place. The Commerce Ministry, which typically releases statements on trade calls, did not respond to a request for comment.

The Japanese yen strengthened 0.08% to 106.03 and the 10-year Treasury yield fell on Tuesday as investors fled to safer assets. The yen's gain was not as strong as Monday's, when it reached a 2-1/2 year high. The yen has gained 3.3% against the dollar this year as the trade war drives traders to safe-haven assets.

"Safer bets are outperforming as the dust settles on trade war developments that left uncertain whether the U.S. and China would strike a deal anytime soon. Persistent trade uncertainty is credited with slowing the global economy and leaving it vulnerable to tipping into recession," said Joseph Manimbo, senior market analyst at Western Union Business Solutions.

The 10-year U.S. Treasury yield fell to a low of 1.500%. It was last at 1.513% while the yield on the two-year yields was at 1.549%, maintaining an inverted yield curve, a sign of a future recession.

The offshore Chinese yuan, sensitive to the U.S.-China trade dispute, was steady on Tuesday after plunging to a record low of 7.1870 against the dollar the day before. It last traded at 7.162.

Global investor Mark Mobius told CNBC on Tuesday that he sees China continuing to "gradually" depreciate its yuan renminbi currency. "They, of course want to keep control and not have a precipitously drop."

"Generally speaking you're going to see a weaker renminbi," said the founder of Mobius Capital Partners, who prior to going out on his own last year spent three decades Franklin Templeton. "Of course, the problem they face is as they reduce the amount of dollar holdings, then it will become much more difficult to keep this control."

Elsewhere, the euro was trading at $1.1097 easing off earlier lows as Italian stocks rallied on hopes that a snap election could be avoided by an arrangement to form a new government in Rome.

The pound was up 0.43% at $1.2266 and by 0.46% against the single currency at 90.44 pence as Britain's opposition Labour Party leader, Jeremy Corbyn, said he would do everything necessary to prevent Britain leaving the European Union without a divorce deal on Oct 31.