* MSCI EM shares index set for best session in three weeks * Rate hike in S.Africa possible either in Sept or Nov - analyst June 23 (Reuters) - Emerging markets stocks jumped 1% on Wednesday after U.S. Federal Reserve Chairman Jerome Powell calmed concerns over policy tightening, while a surge in inflation in South Africa lifted the rand on hawkish central bank expectations. MSCI’s index of EM shares was set for its best session in three weeks after Powell sounded dovish in his testimony to Congress, saying inflation would not be the only determinant in interest rates decisions. “It was enough to let markets move back into their happy place,” said Jeffery Halley, a senior market analyst at Oanda. After a strong session in Asia, Russian shares moved 0.5% closer to all-times highs and South African stocks were on course for their best session this month. Still, the broader EM stocks index is down more than 1% in June after two straight monthly gains as a hawkish turn by the Fed last week led to hefty losses. Higher U.S. interest rates lessen the appeal for riskier emerging markets assets. HAWKISH CHEER FOR RAND Currencies in Turkey, Russia and South Africa firmed between 0.6% and 0.7% as the dollar pulled further away from over two-month highs. South Africa’s rand rose up to 0.9% to hit session highs after data showed headline inflation in May soared to a 30-month high of 5.2%, as expected but above the mid-point of the central bank’s target range of 3%-6%. “Back in May, the (central bank) assessed the risks to its inflation outlook as to the upside. Today’s data shows this risk has realised, emboldening expectations that the central bank could join other EM banks in steadily lifting rates,” said Simon Harvey, FX analyst at Monex Europe. “Depending on the progression of inflation and the health situation in South Africa over the coming months, I think we’re talking about 25-50bps this year ... likely at either or both of the meetings in September and November.” Turkey’s lira cheered central bank governor Sahap Kavcioglu’s announcement late on Tuesday that the country was in talks to secure currency swap agreements with four countries and was close to a deal with two of them. This comes after it increased its existing swap facility with China to $6 billion this month, and tripled its currency-swap agreement with Qatar to $15 billion last year. For GRAPHIC on emerging market FX performance in 2021, see tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2021, see tmsnrt.rs/2OusNdX For TOP NEWS across emerging markets For CENTRAL EUROPE market report, see For TURKISH market report, see For RUSSIAN market report, see (Reporting by Susan Mathew in Bengaluru; Editing by Aditya Soni) Our Standards: The Thomson Reuters Trust Principles.