Emerging market stocks and currencies each hit two-and-a-half week peaks on Monday, after U.S. data on Friday raised hopes of a dovish stance from the Federal Reserve at its meeting this week.

Market participants price in a 99 percent probability of U.S. borrowing costs not being changed on Wednesday, when the Fed's two-day meet ends, with soft U.S. manufacturing data on Friday spurring some expectations of a rate cut later in 2019.

The Fed is also expected to trim its median expectation of rate changes to one hike this year, down from two raises expected earlier, OCBC Bank analysts wrote in a note. They added that the assumption of the Fed moving the expectation to zero hikes this year would be "somewhat presumptuous", though that is OCBC's view.

The situation is a stark departure from 2018, when rising returns on holding dollars combined with the U.S.-China trade war to hit appetite for emerging market assets,  as capital shifted to safer shores in the developed world.

MSCI's index of developing world stocks was up 0.8 percent on the day, while its index of emerging market currencies notched a 0.2 percent rise.

Chinese blue-chip stocks closed 2.9 percent higher, while the Shanghai Composite Index rose 2.5 percent, helped by expectations of a dovish Fed and Beijing's policy boost for growth. The yuan also firmed.

Russia's rouble hit a seven-month high, supported by stronger oil prices and interest in the country's sovereign bonds. Russian stocks ticked up 0.1 percent.

Turkish stocks rose 0.7 percent, helped by gains across most sectors, while the lira dipped 0.3 percent.

House sales in Turkey slid 18.2 percent year-on-year in February, following on from January's drop of nearly a quarter.

South African stocks rose 1.1 percent on gains among materials stocks on concerns of disruptions in the global supply of iron ore.

The rand, however, softened 0.2 percent as continued rolling power cuts by indebted state-owned power utility Eskom weighed on sentiment.

In emerging Europe, stocks broadly gained with a 1.2 percent rise in Hungarian equities on a strong performance by financials setting the benchmark on track for a record closing high.

Romania's leu firmed to its strongest level in nearly a week against the euro. Ratings agency Standard & Poor's on Friday left Romania's credit rating outlook unchanged following an appeal by the country earlier this month.