* Investors shrug off North Korea's latest missile launch
* Fed's Williams: US at or near full employment, price goals
* Euro net long positions rise to highest in over 3 years-IMM
* Sterling inches higher but seen pressured by latest polls
* S Africa's rand jumps after Zuma defeats no-confidence motion
TOKYO, May 29 (Reuters) - The dollar edged higher against a basket of currencies on Monday, moving away from last week's 6-1/2-month lows and shrugging off news of North Korea's latest missile test as investor attention turned to the Federal Reserve's expected interest rate hike next month.
The dollar index, which tracks the U.S. currency against a basket of six major rivals, inched up 0.1 percent to 97.502 , holding well above last week's nadir of 96.797, its lowest since Nov. 9.
San Francisco Federal Reserve President John Williams said in Singapore on Monday that medium-term trends in U.S. inflation remained "pretty favourable," despite some recent soft consumer price data.
The U.S. economy was at or near the Federal Reserve's goals of full employment and stable prices, Williams said, adding that the U.S. central bank wanted to ensure markets stayed calm as the Fed slowly returned interest-rate policy to normal.
Data on Friday indicated the U.S. economy was modestly expanding, which might allow the Fed to raise interest rates further and to begin paring its $4.5 trillion balance sheet.
Gross domestic product grew at an annual 1.2 percent in the first quarter, faster than the 0.7 percent reported last month, though softening business investment and moderate consumer spending might impede an acceleration in the second quarter.
Rates futures implied traders saw a nearly 90 percent chance the Fed would increase rates by a quarter point to 1.00-1.25 percent at its June 13-14 policy meeting, according to CME Group's FedWatch program.
"The market is waiting for the U.S. employment data on Friday," said Masashi Murata, currency strategist for Brown Brothers Harriman in Tokyo.
The nonfarm payrolls report was likely to show that labour market conditions remain solid, which he said "will support the expectation that the Fed is likely to hike rates."
The greenback edged up slightly to 111.37 yen, holding its ground despite a cautious backdrop that usually gives Japan's perceived safe-haven currency a lift.
North Korea fired what appeared to be a short-range ballistic missile on Monday that landed in the sea off its east coast, South Korea's military said, the latest in a series of missile tests defying world pressure and threats of more sanctions.
"The markets are used to news of North Korea's missile tests by now, and the dollar/yen is unlikely to move much unless there is some further escalation of the situation," said Kumiko Ishikawa, FX market analyst at Sony Financial Holdings in Tokyo.
With U.S. and UK markets closed on Monday for the Memorial Day holiday, major currency pairs were likely to tread water, with few incentives to take new positions.
Continuing political turmoil in Washington also kept investors cautious. U.S. President Donald Trump, returning to the White House after a nine-day trip to the Middle East and Europe, attacked the media and dismissed leaks as "fake news" on Sunday, following reports his son-in-law tried to set up a secret channel of communication with Moscow before Trump took office.
The euro edged down 0.1 percent to $1.1165, after notching a 6-1/2-month high of $1.1268 last week.
Net long positioning on the euro rose to its highest in more than three years in the week through May 23, according to calculations by Reuters and Commodity Futures Trading Commission data released on Friday.
Fading political risk in France and a stronger eurozone economy have led to heightened speculation that the European Central Bank may scale back its massive monetary stimulus.
ECB President Draghi is scheduled to speak at the European Parliament later on Monday. Last week Draghi said there was "no reason to deviate from the indications" that the central bank has already laid down.
Britain's pound edged up 0.1 percent to $1.2817 after hitting a three-week low of $1.2775 on Friday in the wake of a poll showing a shrinking lead for the ruling Conservatives ahead of June 8 elections.
The latest weekend polls showed the Conservative Party's lead over the opposition Labour Party has narrowed sharply since last week's terror attack in Manchester, suggesting Prime Minister Theresa May might not win by the landslide predicted just a month ago.
Four opinion polls published on Saturday showed that May's lead had contracted by a range of 2 to 6 percentage points, indicating the election could be much tighter than thought when she called the snap vote.
The South African rand, meanwhile, rose to a two-month high of 12.6300 per U.S. dollar, after South African President Jacob Zuma defeated a no-confidence motion against him at a meeting of top officials of the ruling African National Congress on Sunday.
The greenback was last down 0.5 percent at 12.7925 rand. (Reporting by Tokyo markets team; Editing by Shri Navaratnam and Eric Meijer)