Greece's stock market <.ATG> reopened on Monday after a five-week shutdown brought on by fears the country was about to be dumped from the euro zone, but ended the day with heavy losses.

"If there are continuing significant restrictive measures impacting the accessibility of the Greek equity market by international institutional investors, MSCI may potentially launch a consultation on a proposal regarding the reclassification of the MSCI Greece Index to Standalone Market status from Emerging Markets status," MSCI said in a statement published on its website on Monday.

MSCI's indexes provide a benchmark for more $7 trillion of investments globally, including over $1.7 trillion of emerging market investments. Earlier this month, Greece had an 0.336 percent weight in MSCI's emerging markets index and is 0.035 percent of the global benchmark.

The index provider had asked its clients feedback in early July as to whether whether it should follow its usual practice of waiting 40 days before taking action on Greece's stock market closure or if different treatment is justified.

Index providers S&P Dow Jones and FTSE Russell are also monitoring the situation.

(Reporting by Karin Strohecker, editing by Mike Dolan)