* EM stocks consolidate after best gains in four weeks
* China stocks dip ahead of MSCI decision on index inclusion
* Rand recovers footing after more than 1.5 percent fall Monday
* Hungary c.bank expected to pump more liquidity into markets
LONDON, June 20 (Reuters) - Emerging market stocks took a breather on Tuesday after their best day in almost two months, as investors waited to see whether MSCI would add the first batch of mainland China-listed shares to its $1.5 trillion EM index.
South Africa's rand stabilised too having been spooked by talk of changing the central bank's mandate, Hungary looked set to slosh more cheap money into its banking system, while Russian stocks were on their best run in almost two months.
Taiwan's stock market also hit a 17-year high but the main focus of the day was the potential landmark decision by global index provider MSCI on adding 169 mainland-China listed 'A-shares' to its widely tracked emerging market benchmark.
Though it would represent a token 0.5 percent weighting in the index and represent just 5 percent of the mainland China stocks universe, it would be a symbolic step in recognising China's growing stature in financial markets.
"It is a close call, but in our view they will be added to the index and according to our calculations it could create 7 billion of inflows (over time)," said senior emerging market strategist at Crédit Agricole Guillaume Tresca.
"So it is positive but it is a long-term change, so I don't think it will be a trigger for CNY (yuan) appreciation or anything like that."
Chinese stocks dipped 0.2 percent overnight in Asia , but have risen more than 7 percent over the last month as the MSCI expectations have added to a growing sense that U.S. trade war risks have receded.
Over the past two weeks, an average of 1.2 billion yuan ($177.15 million) has flowed into Chinese shares via the Connect each day, nearly 30 percent more than the average during the Jan-May period.
Away from China, South Africa's rand regained some ground having slumped more than 1.5 percent on Monday after a public watchdog recommended changing the country's constitution to force the central bank to promote economic growth rather than currency and price stability.
It was changing hands at 12.9950 per dollar in morning trade, government bond yields were steady after hitting a three-week high and stocks were down 0.5 percent, having been boosted almost 2 percent by Monday's rout in the rand.
The central bank hit back on Tuesday saying Public Protector Busisiwe Mkhwebane had no business in making recommendations about how it is run.
"The Reserve Bank has consulted its legal team and has been advised that the remedial action prescribed by the Public Protector falls outside her powers and is unlawful," it said.
In central Europe, the Hungarian forint trod water with its central bank expected to keep interest rates at record lows later and pump more liquidity into money markets despite rising wage growth in the country.
The NBH is regarded as one of central Europe's most dovish central banks and a Budapest-based trader said that barring any unexpected developments, the decisions would leave the forint somewhere between 307.30 to 308.50 versus the euro.
"We expect the central bank to really remain on the dovish side," added Crédit Agricole's Tresca.
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; Editing by Janet Lawrence)