MOSCOW, July 28 (Reuters) - Real disposable incomes in Russia grew in annual terms in the second quarter for the first time since early 2020, while unemployment has almost returned to pre-pandemic levels, data showed on Wednesday. Recovery in incomes is a sensitive issue for Russian authorities, particularly ahead of September parliamentary elections, amid the social discontent with high inflation and restrictions related to the COVID-19 pandemic. For years, President Vladimir Putin has promised to raise real disposable incomes, a measure of people"s purchasing power, but they shrank sharply last year due to the coronavirus crisis and the rouble weakening that filtered into consumer prices. Real disposable incomes, which are inflation-adjusted incomes that exclude mandatory payments, increased 6.8% year-on-year in April-June, data from the Federal Statistics Service, or Rosstat, showed. Real disposable incomes have been falling each quarter from the second quarter of 2020 when they staged the deepest decline in decades. After shrinking 3% in 2020, its sharpest contraction in 11 years, the Russian economy has already recovered to pre-pandemic levels, authorities say. But real disposable incomes were still below pre-pandemic levels, the central bank said last month. Rosstat data also showed on Wednesday the official jobless rate in Russia declined in June to 4.8%, its lowest since March 2020, from 4.9% a month earlier. Rosstat also said nominal wages in May declined to 56,171 roubles ($761.54) and provided more details on incomes: RUSSIAN WAGES NOMINAL May 21 April May 20 21 Average wages (roubles) 56,171 56,614 50,747 Yr/yr percent change +9.5 +13.8 +4.0 RUSSIAN WAGES REAL Yr/yr percent change +3.3 +7.8 +1.0 ($1 = 73.7600 roubles) (Reporting by Andrey Ostroukh; Editing by Joe Bavier) Our Standards: The Thomson Reuters Trust Principles.