* U.S. central bank to start two-day policy meeting

* Investors' immediate focus on Germany's ZEW expectation index

* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh

By Daniel Leussink

TOKYO, March 19 (Reuters) - The dollar was under pressure on Tuesday, weighed by growing expectations the Federal Reserve would shift to a more accommodative policy stance this week and concerns about slower U.S. economic growth.

The dollar index, which measures the greenback against a basket of six major currencies, was a shade lower at 96.495, hovering close to a two-week low. The index has lost 1.2 percent after hitting a three-month high of 97.710 on March 7.

The dollar has weakened in recent sessions on growing expectations the Fed will strike a dovish tone at its two-day policy meeting due to start later on Tuesday.

Many investors expect the Fed, which has raised rates four times last year, to keep its benchmark overnight interest rate unchanged and stick to its pledge of a "patient" approach to monetary policy.

Masafumi Yamamoto, chief currency strategist at Mizuho Securities, said while the market is expecting more accommodative sentiments from the meeting, equity markets were unlikely to react positively to such a development.

"If the Fed really shows a gloomy outlook for growth and rates, then it's also a negative for U.S. equities. Then that will be a negative for the dollar," Yamamoto said.

"There is a high risk that whichever the outcome is, it will push down dollar/yen."

As the dollar took a breather, other major currencies advanced by default. The yen rose 0.1 percent to 111.27 yen per dollar, extending its gains to a third session.

Sterling also gained, rising 0.1 percent to $1.3268. It had seesawed overnight after the speaker of Britain's parliament said Prime Minister Theresa May's Brexit deal could not be voted on again unless a different proposal was submitted.

The Bank of England is expected to leave its interest rate outlook unchanged at a policy meeting on Thursday due to the deep uncertainty over Britain's decision to leave the European Union.

The euro was down a tad at $1.1335.

Investors' focus on Tuesday was also on Germany's ZEW economic index for March, due for release around 1000 GMT.

The German economy, Europe's largest, barely avoided recession in the final quarter of last year, as the negative impact from global trade disputes and Brexit weighed on a decade of expansion.

"The ZEW expectation index has been improving for four consecutive months," said Mizuho's Yamamoto.

"If another month's improvement is shown, then I think that will be quite positive for the euro."

(Editing by Sam Holmes)