* Onshore yuan hits 14-month high
* EM stocks heading for eighth monthly gain
* Russia stocks, rouble up after Otkritie bank bailout
LONDON, Aug 30 (Reuters) - Emerging market stocks climbed back toward a three-year high and were heading for their longest run of monthly gains since 2003 on Wednesday, as nerves triggered by North Korea's latest missile launch began to recede.
China's yuan was also in focus as Beijing pushed it to a 14-month high, as were Russian banks after authorities there launched one of the biggest banking bail-outs in the country's history on Tuesday.
MSCI's 24-country emerging market stocks index was up 0.6 percent with rouble-denominated Russian stocks up the same and the rouble up 0.3 percent following the rescue of struggling private lender Otkritie.
Shares in Otkritie fell 0.75 percent after a 2.4-percent rise the previous day when the central bank announced its bailout.
Traders were still waiting for more information on the deal, but Tuesday's relief rally had come as Russia's central bank said it would effectively fund the rescue, rather than use new rules to make bond holders foot the bill.
Chief CEE economist at UniCredit Lubomir Mitov said it stopped worries escalating around other potentially troubled banks.
"The whole idea is to create some sense of stability in the banking system because I don't think the central bank would risk creating even minor perception that deposits are not safe,"
"I personally would never expect that the bail in would be used here. Firstly the bank is too big, second a bail in especially of subordinated debt holders would really reverberate through the system and could be a very bad signal for the ability of the Russian banks to raise capital."
The gradual return in global risk appetite saw the dollar shuffle higher, which beat back 'high-yielding' EM currencies like the Turkish lira and South African rand.
South Africa's private sector credit demand growth slowed to 5.71 percent in July from 6.16 percent in June, central bank data showed on Wednesday.
It had been a mixed day for other EM FX markets.
South Korea's won regained 0.4 percent of the 0.6 percent it lost following Pyongyang's missile launch, a rally in copper kept Chile's peso at a 2-year high though a strong Chinese yuan remained the bigger focus.
It had climbed to a 14-month high against the dollar on Wednesday, after the central bank set a sharply firmer official guidance midpoint rate of 6.6102 per dollar, the strongest since Aug. 17, 2016.
That sent the spot 'onshore' yuan rate as high as 6.60 per dollar in early trade before dipping back to 6.5910.
The onshore yuan has gained 2.2 percent against the dollar so far this month, a sizable gain for a currency that typically trades in a wafer-thin range.
The renminbi is also set for its biggest monthly gain since 1994, when China unified official and market exchange rates and price data was available.
For GRAPHIC on emerging market FX performance 2017, see http://tmsnrt.rs/2e7eoml For GRAPHIC on MSCI emerging index performance 2017, see http://tmsnrt.rs/2dZbdP5
For CENTRAL EUROPE market report, see
For TURKISH market report, see
For RUSSIAN market report, see)
(Reporting by Marc Jones; Graphic by Claire Milhench; Editing by Andrew Heavens)