* European shares hold at 21-month highs, lift off day's lows
* Wall Street set to open slightly lower
* Dollar dips vs peers on FBI director's dismissal
* Greek yields hit lowest since 2012 debt restructuring
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Nigel Stephenson
LONDON, May 10 (Reuters) - European shares held at 21-month highs on Wednesday, while the dollar fell on concerns that U.S. President Donald Trump's dismissal of his FBI chief could make passage of his tax reform plans more difficult.
Wall Street looked set to open lower, with index futures down about 0.2 percent .
Expectation-beating first-quarter company results have lifted stock markets across the globe, with European full-year earnings forecasts set to be their best since 2010. The prospect of U.S. tax cuts has also helped push shares higher.
At the same time, measures of market volatility are at rock-bottom. The U.S. VIX index fell on Tuesday to 9.56, its lowest since late 2006. [reut.rs/2pja9xd ]
However, Trump's abrupt sacking of FBI Director James Comey marked a fresh intrusion of politics into markets after Emmanuel Macron's weekend victory in the French presidential election had seemed to clear the decks of major political risk, at least in Europe.
"This is a political story rather than a market story, but yet again it creates uncertainty in the market, which leaves everything the president does with a cloud floating over it," said James Hughes, chief markets analyst at GKFX in London.
The pan-European STOXX 600 index was fractionally up on the day, having traded in the red for most of the morning, weighed down by construction and materials stocks and by Italian banks. The index hit its highest since August 2015 on Tuesday.
Asian shares, however, edged up for a third consecutive day. MSCI's main index of Asia-Pacific shares, excluding Japan rising 0.1 percent, having earlier matched a two-year high hit last week.
Twelve-month forward earnings-per-share for the index is at its highest level in more than three years.
South Korean stocks led losers as investors took profits after liberal leader Moon Jae-in was elected president, while Chinese shares closed lower after factory gate prices in the world's second-biggest economy cooled more than expected in April.
Tokyo shares hit a 17-month high, up 0.3 percent on the day as a relatively weak yen outweighed concerns triggered by Trump's sacking of Comey.
The U.S. president said he had fired Comey, who had been leading an investigation into the Trump 2016 campaign's possible collusion with Russia, over his handling of an email scandal involving then-Democratic candidate Hillary Clinton.
The dollar fell 0.1 percent against a basket of major currencies after slipping on the view that political uncertainty could derail Trump's tax reform plans.
The yen, often sought in times of market uncertainty, was last 0.2 percent higher at 113.79 to the dollar. The euro was flat at $1.0868. The safe-haven Swiss franc also rose against the euro and dollar.
Falling U.S. Treasury yields also weighed on the dollar. Ten-year yields were down 3.1 basis points at 2.38 percent after retreating from five-week highs touched on Tuesday as investors made room in their portfolios for new issuance of government and corporate debt.
The most eye-catching move in euro zone government bond markets was a fall in Greek 10-year yields to their lowest since its debt was restructured in 2012.
Athens and its creditors reached a deal this month on reforms that could trigger the release of more rescue funds.
"There is a relief that Greece will get its disbursements to get through the summer, and that is the main driver of the bond rally," ING's senior rates strategist Martin van Vliet said.
Oil prices rose after Saudi Arabia said it would cut supplies to Asia and U.S. inventories fell more than expected. Brent crude was last up 48 cents at $49.21 a barrel.
Gold rose 0.2 percent to $1,223 an ounce.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by Saikat Chatterjee in Hong Kong, Jamie McGeever, John Geddie in London; Editing by Andrew Heavens