* Asian stock markets : tmsnrt.rs/2zpUAr4
* Wall St advance, dollar flat as traders brace for a dovish Fed
* Pound drifts as UK parliament bans vote on same Brexit deal
* European shares seen opening slightly softer
By Tomo Uetake
TOKYO, March 19 (Reuters) - Asian shares held to tight ranges on Tuesday ahead of a Federal Reserve policy meeting, but were broadly supported near 6-1/2-month highs on expectations the U.S. central bank might strike a dovish tone, while fresh Brexit worries weighed on the pound.
European shares were expected to open slightly lower, with financial spread-betters seeing Britain's FTSE, France's CAC and Germany's DAX ticking down between 0.03 and 0.12 percent each.
MSCI's broadest index of Asia-Pacific shares outside Japan was virtually flat, easing back from its highest level since Sept. 4 hit earlier in the session.
Japan's Nikkei average and Australian stocks both dipped 0.1 percent.
In China, the benchmark Shanghai Composite slipped 0.2 percent and the blue-chip CSI 300 fell 0.4 percent, while Hong Kong's Hang Seng was almost flat.
All three major Wall Street indexes rose overnight, lifted by the bank and tech sectors, with the Dow Jones Industrial Average, the S&P 500, and the Nasdaq Composite adding between 0.3 and 0.4 percent each.
"Speculators appear to be betting on a rise in stock prices on the back of a dovish Fed. The Fed is unlikely to kill such hopes. Yet there is a risk the Fed could tone down its dovishness," said Masanari Takada, cross-asset strategist at Nomura Securities.
With global economic growth appearing to slow, traders were focused on the Fed, which kicks off a two-day policy meeting later in the day, for clues about the likely path of U.S. borrowing costs.
Investors will particularly look to see whether policymakers have sufficiently lowered their interest rate forecasts to more closely align their "dot plot", a diagram showing individual policymakers' rate views for the next three years.
Also expected is more detail on a plan to stop cutting the Fed's holdings of nearly $3.8 trillion in bonds.
"A key focus is when the Fed will omit the word 'patient' from its statement, as that would be a pre-requisite for a rate hike," said Toru Yamamoto, chief fixed income strategist at Daiwa Securities.
In currency markets, sterling found some footing after slipping to as low as $1.3183 in the previous session as lawmakers cast doubt on Prime Minister Theresa May's third attempt to get parliament to back her Brexit deal.
May's Brexit plans were thrown into further turmoil on Monday when the speaker of parliament ruled that she could not put her divorce deal to a new vote unless it was re-submitted in fundamentally different form.
May has only two days to win approval for her deal to leave the European Union if she wants to go to a summit with the bloc's leaders on Thursday with something to offer them in return for more time.
Meanwhile, senior diplomats said the European Union leaders could hold off making any final decision on any Brexit delay when they meet in Brussels later this week, depending on what exactly May asks them for.
The dollar index against a basket of six major currencies eased 0.1 percent to 96.450, hovering close to a two-week low. The index has lost 1.2 percent after hitting a three-month high of 97.710 marked on March 7.
The Japanese yen inched up 0.1 percent to 111.28 yen to the dollar, while the euro was almost flat at $1.1347.
Oil prices were near 2019 highs, supported by supply cuts led by producer club OPEC. U.S. sanctions against oil producers Iran and Venezuela are also boosting prices, although traders said the market may be capped by rising U.S. output.
U.S. West Texas Intermediate (WTI) futures eased 0.1 percent to $59.01 per barrel, close to the 2019 high of $59.23 reached the previous day, while Brent crude futures were little changed at $67.58, also not far from this year's high of $68.14.
Reporting by Tomo Uetake; Additional reporting by Hideyuki Sano; Editing by Kim Coghill and Sam Holmes