(Corrects day in first paragraph to Wednesday)
* European stocks edge down
* Wall Street pulls back from this week's record highs
* US yield curve at its steepest in around 3 weeks
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Dhara Ranasinghe
LONDON, Dec 20 (Reuters) - World stock markets wavered just below recent record highs while U.S. Treasury yields held near multi-month peaks on Wednesday as the final procedural throes of long-awaited U.S. tax reform played out in Washington.
The Republican-led U.S. Senate approved the sweeping $1.5-trillion tax bill in the early hours of Wednesday. A re-vote by the House of Representatives was scheduled for later in the day, with approval expected, and the bill will then go to President Donald Trump to sign into law.
European stock markets nudged lower, with blue-chip indexes in Germany, France and Britain flat to a touch weaker on the day.
In Asia, MSCI's broadest index of Asia-Pacific shares outside Japan bobbed lower in a choppy session, while Japan's Nikkei index finished up 0.1 percent.
MSCI's world equity index, which tracks shares in 47 countries, was little changed and holding just below record highs hit on Monday.
U.S. Treasury yields, which notched up their biggest one-day jump in almost three months on Tuesday as the tax bill moved towards passage, steadied at around 2.46 percent -- holding near the previous day's highs.
"Last week the reaction of bond markets was one of ambivalence about the likelihood of these measures getting passed," said Michael Hewson, chief market analyst at CMC Markets in London.
"However, U.S. yields have jumped sharply higher in the last two days as the prospect of higher inflation and growth prompted some positioning adjustments in anticipation that the measures, if passed, could prompt conditions that might see rates have to rise faster than expected next year."
Republicans, who control both lawmaking chambers, said their tax plan would boost consumer spending and business investments, while independent government estimates showed the proposed tax cuts would end up adding at least $1 trillion to the $20 trillion national debt in 10 years.
Europe's bond markets were also nursing losses after a heavy selloff on Tuesday that saw Germany's long-dated yields rise to three-week highs after the euro zone's benchmark bond issuer announced plans to issue more longer-dated debt next year.
The euro got a lift from higher euro zone rates, gaining 0.5 percent on Tuesday, when central bank governors of Estonia, Slovakia and Germany all discussed the need to shift the debate from bond purchases to other tools such as interest rates.
"That's re-igniting the debate about ECB tightening, so despite the outlook for the U.S. tax bill passage, euro-dollar is strong right now," Masafumi Yamamoto, chief currency strategist for Mizuho Securities in Tokyo.
Against a basket of six rival currencies, the dollar was a touch lower on the day at 93.418.
The greenback edged down 0.2 percent to 113.11 yen, while the euro was a touch firmer at $1.1850.
Bitcoin was almost 4 percent lower on the Bitstamp exchange at $17,007, after earlier losing almost one-fifth of its value from a peak hit just three days ago.
Sweden's crown briefly surged as much as 1 percent after the central bank kept rates unchanged but said it would reinvest coupons and cash from maturing bonds, including bringing forward some reinvestments into 2018.
Elsewhere, U.S. crude oil futures extended gains, helped by a North Sea pipeline outage, OPEC-led supply cuts and expectations that U.S. crude inventories had fallen for a fifth week.
U.S. crude was up 0.3 percent, or 15 cents, at $57.71 a barrel, while Brent crude was 0.2 percent higher.
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
Reporting by Dhara Ranasinghe; additional reporting by Lisa Twaronite in TOKYO; Editing by Catherine Evans