* U.S. stocks holding slight gains
* Trump at UN says U.S. may have to 'totally destroy' N. Korea
* Fed seen announcing plans to unwind debt portfolio
* Oil edges off recent high ahead U.S. stock data, OPEC meeting
* Nikkei scales over 2-yr high on weak yen, snap election hope (Updates prices, adds European shares' close)
NEW YORK, Sept 19 (Reuters) - Global stock markets edged higher on Tuesday and the dollar dipped as investors awaited signals from the U.S. Federal Reserve on when it will hike interest rates again and start shrinking its balance sheet.
Wall Street stocks gained slightly, with the Dow climbing to a fresh record, while an index of stocks across the globe also inched higher.
Tuesday marks the start of the U.S. central bank's two-day meeting. The Fed is widely expected to announce on Wednesday that it will begin paring its bond holdings, with reductions likely to start in the coming months.
Investors will also be watching for signals that the Fed will raise rates in December, and for any clues on personnel changes as the end of Fed Chair Janet Yellen's term approaches and after the resignation of Vice Chair Stanley Fischer earlier this month.
"The quiet nature of (the market) is in anticipation of the Fed meeting. Janet Yellen has a press conference. That and the statement will perhaps provide some insight into what they're going to do in terms of deleveraging their balance sheet," said Bucky Hellwig, senior vice president at BB&T Wealth Management in Birmingham, Alabama.
"There's some concern among investors as to how this will work, and how it will affect long-term rates."
The Fed's possible move to further roll back stimulus has not stemmed the greenback's weakness this year as other major central banks are considering steps to either slow their bond purchases or raise interest rates.
The dollar had weakened against yen ahead of U.S. President Donald Trump's speech before the United Nations General Assembly.
In the speech, Trump warned that the United States will be forced to "totally destroy" North Korea unless Pyongyang backs down from its nuclear challenge, but the criticism was not enough to spook investors.
The greenback was steady at 111.57 yen, below its eight-week peak of 111.87 set earlier Tuesday.
A dollar index fell 0.14 percent.
Weighing on the dollar index earlier was U.S. data showing domestic home construction fell for a second straight month in August.
The Dow Jones industrial average rose 45.56 points, or 0.2 percent, to 22,376.91, the S&P 500 gained 3.12 points, or 0.12 percent, to 2,506.99 and the Nasdaq Composite added 7.22 points, or 0.11 percent, to 6,461.86.
"It's not a really big move to the upside, (but) stocks still look attractive relative to other investments," Hellwig said.
The S&P 500 and Dow had both hit new peaks on Monday despite some late pressure on big tech stocks.
The pan-European FTSEurofirst 300 index closed up 0.1 percent, while MSCI's gauge of stocks across the globe gained 0.20 percent.
Tokyo's Nikkei surged 2 percent to its highest close in more than two years as investors drew confidence from a weakening yen and hopes of a snap election underpinned the market.
In the U.S. bond market, prices were near flat. Benchmark 10-year notes last fell 4/32 in price to yield 2.2428 percent, from 2.23 percent late on Monday.
In energy markets, oil prices retreated from near-five-month highs in advance of data expected to show a build in U.S. crude inventories. Also, refineries were still restarting after recent storm activity.
U.S. crude fell 1.06 percent to $49.38 per barrel and Brent was last at $54.74, down 0.92 percent on the day.
(Additional reporting by Marc Jones and John Geddie in London; Editing by Dan Grebler and Nick Zieminski)