At 1500 GMT, the rand traded at 15.3200 against the dollar, down around 0.4% from its previous close. The dollar was up 0.3% against a basket of currencies.
Markets had until recently mostly shrugged off a build-up of Russian troops near Ukraine's borders, but tensions have ratcheted up lately. NATO said on Monday it was putting forces on standby and reinforcing eastern Europe with more ships and fighter jets, while Russia denounced Western "hysteria".
The U.S. Federal Reserve begins a two-day policy meeting later on Tuesday, and investors will study its statement for hints about the timing and pace of interest rate hikes.
Limiting rand losses, on Thursday South Africa's central bank is expected to raise rates by 25 basis points to 4.00% in response to rising inflation, according to a Reuters poll published last week.
The currency reacted little to data showing a leading business cycle indicator rose 0.6% month-on-month in November.
Shares on the Johannesburg Stock Exchange (JSE) edged up on the day as investors moved away from fears around the potential Ukraine conflict and focused on the expected Fed meeting and local interest rate decision.
The benchmark all-share index closed up 0.21% at 72,315 points while the blue-chip index of top 40 companies ended up 0.33% at 65,870 points.
The government's benchmark 2030 bond fell, with the yield rising 6.5 basis points to 9.365%.
(Reporting by Promit Mukherjee and Alexander Winning; Editing by Susan Fenton)
