* Equities move lower in U.S. and Europe
* Dollar drops to 6-1/2-month low versus currency basket
* Tension between Russia, Ukraine weighs on markets (Updates prices to U.S. close)
NEW YORK, May 6 (Reuters) - Stock markets around the world fell on Tuesday, with U.S. shares extending declines in afternoon trading as persistent worries over the instability in Ukraine pushed investors to take profits with major indexes still near record levels.
The U.S. dollar fell 0.47 percent to a 6-1/2-month low against a basket of currencies, while U.S. bond yields struggled to pull out of recent troughs and the yen and euro both gained.
On Wall Street, financial shares fell following disappointing results from American International Group, and a selloff at Twitter Inc weighed on tech shares. Even so, the Dow and S&P 500 remained within striking distance of record levels.
Investors kept an eye on the unrest in Ukraine, where more than 30 pro-Russian separatists were killed in fighting near the east Ukraine rebel stronghold of Slaviansk, according to the interior minister. Russia announced plans to beef up its Black Sea warship fleet.
"Valuations are close to the ceiling and some people may be uncomfortable because of that, especially given growing nervousness over the geopolitical tensions," said Bernard Baumohl, managing director and chief global economist at the Economic Outlook Group in Princeton, New Jersey. "However, we still have room to grow before alarm bells start going off."
The Dow Jones industrial average was down 129.53 points, or 0.78 percent, at 16,401.02. The Standard & Poor's 500 Index was down 16.94 points, or 0.90 percent, at 1,867.72. The Nasdaq Composite Index was down 57.30 points, or 1.38 percent, at 4,080.76.
The benchmark 10-year U.S. Treasury note was up 4/32 in price, with the yield at 2.5951 percent.
The euro rose 0.4 percent to $1.3930. The yen rose 0.5 percent against the dollar to 101.63 yen.
European shares fell 0.3 percent, while the MSCI International ACWI Price Index slipped 0.2 percent.
Gold dipped 0.2 percent following a sharp rally over the previous two sessions. Wheat prices, which have been tied to the situation between Russia and Ukraine, both of which are big grain producers, rose for a third straight session, up 1.4 percent.
In Europe, the European Central Bank is expected to repeat its concern about the impact of the strong euro on already-low inflation when it meets on Thursday, though economists doubt the ECB will cut record-low interest rates again.
Yields on peripheral countries' lower-rated bonds remained at multi-year lows, and in some cases all-time lows. Investors welcomed Portugal's plan to exit its bailout and continued to bet on some future easing of ECB monetary policy. (Editing by Dan Grebler and Leslie Adler)