* Russian c.bank hikes rates by 350 bp to 12%

* China cuts rates after weak batch of July economic data

* EM stocks fall 0.5%, currencies ease 0.4%

Aug 15 (Reuters) - Russia's rouble gave up early gains on Tuesday after the central bank's emergency rate hike, while Chinese stocks closed lower on economic slowdown fears even as the central bank unexpectedly cut key policy rates to support growth.

Russia's central bank hiked its key interest rate by 350 basis points to 12%, an emergency move to try and stop the rouble weakening past 100 to the dollar after a public call from the Kremlin for tighter monetary policy.

The rouble erased its intraday gains after the decision, and was last down 0.4% at 98.03.

"It is an emergency response to the fall in the value of the rouble, which has recently suffered one of the fastest depreciations of EM currencies," said Stuart Cole, chief macro economist at Equiti Capital.

"While such a depreciation risks boosting inflation, it is also the signal it sends out to the Russian public about the costs of the invasion of Ukraine. As such, today's decision will likely have had an element of politics behind it as well as economics." The rouble, which has lot more than a fifth of its value against the dollar since the start of the Ukraine war, hit a near 17-month low of 101.75 on Monday and briefly traded at 92.60 on Tuesday morning, swinging wildly as the market reacted to the central bank's sudden intervention.

In Asia, a slew of Chinese economic data highlighted intensifying pressure on the world's second-largest economy from multiple fronts, prompting Beijing to cut key policy rates to shore up activity.

China's blue-chip CSI 300 Index and Hong Kong's Hang Seng Index fell 0.2% and 1% respectively, while the yuan also weakened and briefly hit a nine-month low.

Some investors are slashing their exposure to China.

Regulatory filings showed U.S.-based hedge fund investors including Coatue, D1 Capital and Tiger Global cut their exposure to Chinese companies in the second quarter, as the country's economic prospects seemed to wobble and geopolitical tension increased.

Overall, the MSCI's index for emerging market stocks shed 0.5%, while the currencies index eased 0.4%.

The Turkish lira was unchanged against the dollar, while South Africa's rand weakened 0.6% on worries about the health of China, its largest trading partner.

Central and eastern European currencies weakened against the euro, with the Hungarian forint leading losses.

Data showed Hungary's final industrial output fell 3.8% year-on-year in June, unchanged from the first estimate.

Saudi Arabia's annual inflation rate eased for a second consecutive month to 2.3% in July from 2.7% in June, government data showed.

(Reporting by Bansari Mayur Kamdar in Bengaluru; Editing by Sharon Singleton)