* Rouble recoups all declines from last week

* S.African rand rises, inflation eases in Jan

* MSCI EM stock index eyes best day in 1-week

Feb 16 (Reuters) - Emerging market stocks eyed their best day in one week on Wednesday, while Russia's rouble gained for a third straight session, as fears of a Russian invasion of Ukraine waned.

The rouble strengthened 1.1% against the dollar, recouping all of its declines from last week, which also saw global financial markets slammed by heightening geopolitical tensions between Russia and Ukraine.

Moscow's signal to return some troops to base from near the Ukrainian border buoyed investor sentiment, boosting emerging market stocks by 1.4% and weakening safe-haven bets including the dollar.

The West has responded with caution and scepticism to Russia's move, with investors still viewing it as a tentative positive for financial markets.

"We're only reading headlines but the tone has softened... the risk is still there but every day we see that the troops are leaving, or they are turning and about to leave," said Elena Lovén, senior fund manager at Swedbank Robur.

"The problem is we don't know exactly what's happening at the border."

However, Lovén remains constructive on the rouble and other Russian assets on expectations of a diplomatic solution to the issue.

Russia's dollar denominated RTS share index gained 2.8%, while the rouble-based MOEX index added 1.7%.

Ukraine's hryvnia gained 0.6% against the dollar, for the second straight day, and its dollar-denominated government bonds also rose about 3%.

South Africa's rand rose 0.2%. Data showed consumer inflation fell to 5.7% year on year in January from 5.9% in December, in line with expectations, but still towards the upper end of the central bank's 3%-6% target range.

"Over the past weeks, ZAR was able to appreciate in line with other EM currencies. The fact that the SARB started hiking interest rates early on is likely to support ZAR," You-Na Park-Heger, FX and EM analyst at Commerzbank, wrote in a note.

"I think that once the Federal Reserve starts its rate hike cycle in March, ZAR will ease against USD."

Investors awaited the release of the minutes from the U.S. Federal Reserve's January policy meeting later in the day for clues on the course for the central bank's rate hiking cycle.

For GRAPHIC on emerging market FX performance in 2022, see http://tmsnrt.rs/2egbfVh

For TOP NEWS across emerging markets

For CENTRAL EUROPE market report, see

For TURKISH market report, see

For RUSSIAN market report, see

(Reporting by Shreyashi Sanyal in Bengaluru; Editing by Rashmi Aich)