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* Post-Brexit equity market recovery stalls
* STOXX 600 set for worst month since last August
* Dt Bank, Santander fall after U.S. stress test blow
By Sudip Kar-Gupta
LONDON, June 30 (Reuters) - European shares fell on Thursday, with a recovery from a heavy sell-off caused by Britain's vote to leave the European Union last week stalled as shares in major banks lost more ground.
The pan-European STOXX 600 index and the similar FTSEurofirst 300 index both fell by 0.6 percent. The STOXX 600 and FTSEurofirst are both down around 10 percent since the start of 2016.
The STOXX 600 was also down around 7 percent this month, and was set to post its worst monthly performance since August 2015.
Banking stocks were among the worst performers.
Shares in Deutsche Bank and Santander fell 4 percent and 2.9 percent respectively after their U.S units suffered the ignominy of failing U.S. stress tests again this year.
Royal Bank of Scotland, down more 30 percent since the June 24 voting result showed that Britain had opted to leave the EU, also fell another 4 percent after Morgan Stanley cut its rating on the stock to "equal weight" from "overweight".
The STOXX 600 slumped 11 percent over the course of June 24 and June 27, but then recovered 6 percent over Tuesday and Wednesday, helped by signs that politicians were in no rush to start Britain's formal exit from the EU, dubbed as 'Brexit'.
Nevertheless, many investors remained wary of European equities, given the political uncertainty triggered by the Brexit vote, which led to Britain's Prime Minister resigning and concerns of general political instability across Europe.
"It's not the time to be buying European stocks. I'd prefer to allocate my assets towards U.S. equities," said Andreas Clenow, chief investment officer of ACIES Asset Management in Zurich.
Strategists at Wall Street bank Citigroup also cited the political uncertainty caused by the Brexit fall-out as a reason to stay "underweight" on stocks.
"With equity market moves quite limited thus far and our global growth forecasts still falling, we think this uncertainty may see both lower earnings and lower ratings, so we increase our global equity underweight," Citi wrote in a note. (Editing by Keith Weir)