* Lira falls as much as 0.4%, June inflation at 2-year high
* EM stocks muted
* Rand, rouble fall on sluggish PMI readings
By Ambar Warrick
July 5 (Reuters) - Turkey's lira, and most currencies in Europe, the Middle East and Africa fell on disappointing economic readings, while broader emerging market currencies gained on Monday as mixed U.S. labour data weighed on the dollar.
MSCI's index of emerging market (EM) currencies rose about 0.3% and was set to snap a five-day losing streak, with the dollar stalling on signs of weakness in the labour market, which is a key factor for the Federal Reserve to consider tightening policy.
Data showing rising U.S. unemployment cut short a dollar rally last week and helped emerging market assets, which had been under pressure from some hawkish signals from the Fed.
But currencies in Europe, the Middle East and Africa (EMEA) traded lower on Monday, with Russia's rouble falling 0.4% to 73.3575 to the dollar, as weakness in oil prices weighed.
Russia's service sector expanded in June for a sixth straight month, but the pace of growth appeared to be slowing.
Turkey's lira gave up early gains and fell as much as 0.4% versus the dollar to 8.7105, after inflation rose much more than expected to 17.53% in June, its highest in two years.
That puts pressure on the Central bank of Turkey (CBT) to hike interest rates and support the lira, but also sets up an inevitable clash with President Tayyip Erdogan's unconventional view that high interest rates cause inflation.
"The likelihood of CBT cutting rates voluntarily will disappear, but that will bring the central bank closer to a showdown with the President... CBT has, so far, stuck to a rather hawkish rhetoric in defiance of pressure from the president, which has supported the lira," said Tatha Ghose FX and EM analyst at Commerzbank.
Lira depreciation had accelerated after Erdogan sacked a hawkish central bank governor in March, the most recent firing in a string of governors over the past two years.
South Africa's rand eased 0.1% after data showed South African private sector activity expanded at a slower rate in June, due to disruptions caused by new COVID-19 measures.
In central Europe, Hungary's forint and the Czech crown rose slightly against the euro. Both currencies have been supported by hawkish central banks this year.
Emerging market stocks traded flat, with MSCI's index inching 0.04% lower.
Most EMEA stocks traded along similar lines, as a holiday in the United States made for a dearth of immediate cues.
For GRAPHIC on emerging market FX performance in 2021, see http://tmsnrt.rs/2egbfVh For GRAPHIC on MSCI emerging index performance in 2021, see https://tmsnrt.rs/2OusNdX
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For CENTRAL EUROPE market report, see
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For RUSSIAN market report, see
(Reporting by Ambar Warrick; Editing by Kirsten Donovan)