SHANGHAI, May 25 (Reuters) - China"s yuan jumped to a near three-year high against a weaker dollar on Tuesday, although investors are now gauging the central bank"s tolerance for a firmer currency before chasing new highs. The onshore yuan opened at 6.4110 per dollar and jumped to a high of 6.4030, the strongest level since June 2018 and a tad below the psychologically important 6.4 per dollar level. By midday, it was changing hands at 6.4117, 83 pips firmer than the previous late session close. "The RMB still sees the firmest appreciation pressure, and this translates to the 6.4000 being still in the spotlight," strategists at OCBC Bank said in a note. Several traders said the yuan"s strength reflected the greenback"s overnight weakness following softer-than-expected U.S. data and affirmations from Federal Reserve officials that policy would stay on hold. But the onshore spot yuan was stuck at around 6.41 per dollar level after leaps in initial trade as investors worried a too rapid rise in the currency could prompt state-run banks to step in to rein in strength. Rapid yuan moves in either direction are not ideal for the central bank, said a trader at a Chinese bank. Many analysts and economists said a too strong yuan could hurt the country"s exporters despite external trade remaining resilient in the first quarter of this year. "In our view, the People"s Bank of China (PBOC) is aware of the RMB appreciation risk given slowing China (economic) growth momentum in Q1 and still uneven recovery," said Ken Cheung, chief Asian FX strategist at Mizuho Bank in Hong Kong. "The CNY fixings in coming days will be monitored for any PBOC FX policy guidance." Markets believed that the official midpoint fixing is one of the key signals showing authorities" attitude toward the yuan"s levels. Prior to market opening on Tuesday, the PBOC set the midpoint rate at 6.4283 per dollar, 125 pips or 0.19% firmer than the previous fix of 6.4408. It was 23 pips weaker than Reuters" estimate of 6.426. The PBOC over the weekend urgently reiterated no change to the currency policy after comments from central bank researchers that had unnerved the market. One researcher felt China should free up the exchange rate over time to support wider global adoption of the currency, while another said the exchange rate target could be dropped to allow further strengthening to offset rising commodity prices. The offshore yuan also followed its onshore counterpart"s appreciation in morning trade to test the key 6.4 per dollar level. It jumped to a high of 6.4010 before trading at 6.406 per dollar as of midday. The global dollar index fell to 89.759 at midday from the previous close of 89.855. The yuan market at 0400 GMT: ONSHORE SPOT: Item Current Previous Change PBOC midpoint 6.4283 6.4408 0.19% Spot yuan 6.4117 6.42 0.13% Divergence from -0.26% midpoint* Spot change YTD 1.82% Spot change since 2005 29.08% revaluation Key indexes: Item Current Previous Change Thomson 97.53 97.33 0.2 Reuters/HKEX CNH index Dollar index 89.759 89.855 -0.1 *Divergence of the dollar/yuan exchange rate. Negative number indicates that spot yuan is trading stronger than the midpoint. The People"s Bank of China (PBOC) allows the exchange rate to rise or fall 2% from official midpoint rate it sets each morning. OFFSHORE CNH MARKET Instrument Current Difference from onshore Offshore spot yuan 6.406 0.09% * Offshore 6.566 -2.10% non-deliverable forwards ** *Premium for offshore spot over onshore **Figure reflects difference from PBOC"s official midpoint, since non-deliverable forwards are settled against the midpoint. . (Reporting by Winni Zhou and Andrew Galbraith; Editing by Sam Holmes) Our Standards: The Thomson Reuters Trust Principles.