Emerging market stocks gave up gains on Friday after strong U.S. jobs data strengthened the case for the Federal Reserve to stay aggressive with monetary policy.

MSCI's index of emerging market stocks which had risen up to 0.5% in the session, was last trading flat. Most Latin American bourses fell between 0.04% and 0.9%, in line with a drop on Wall Street.

In signs of a tight U.S. labor market, data showed nonfarm payrolls rose by 390,000 jobs last month, while the unemployment rate held steady at 3.6%, both topping consensus estimates.

"We don't believe the May payroll report changes the calculation for the Fed, supporting their inclination to front-load interest rate hikes until it reaches a more neutral stance by the fall," said strategists at TD Securities. "We continue to expect the (Fed) to increase rates by 50 basis points in both the June and July, and to deliver a 25bp hike at each meeting between September and March 2023."

But the emerging markets index is still on course to mark its third straight week with gains. Developing world currencies came off session lows as the dollar, which rose up to 0.5% after the data, traded flat.

Some Asian currencies were in negative territory, while Turkey's lira and South Africa's rand fell around 0.3% each. Market holidays in China and the UK made for subdued volumes. The artificially propped up Russian rouble rose in offshore trade, while Latin American currencies climbed with the Mexican peso up 0.1% after having hit session highs.

In Turkey, data showed inflation jumped to a 24-year high of 73.5% in May, fuelled by the war in Ukraine, rising energy prices and a tumbling lira, though the figure was slightly lower than economists had predicted. The lira weakened to 16.53 against the dollar touching its lowest since December. The local currency tumbled 44% in 2021 and another 20% so far this year.

"May inflation showed no respite with continuing broad-based pricing pressures mainly driven by an accommodative monetary policy stance, while risks remain at the forefront with ongoing geopolitical issues and a less supportive global backdrop, that adds to challenges to the currency outlook," said Muhammet Mercan, chief economist, Turkey, at ING. "Given the increasing and rapid FX pass-through observed in recent months, currency moves will be key for inflation."

Elsewhere, Brazil's real swung between losses and gains, last up 0.1% at 4.7819 per dollar. Data showed industrial production in Brazil rose slightly in April from March, in line with economists' estimates.

(Reporting by Susan Mathew in Bengaluru, Editing by Frances Kerry)