* Investors shrug off North Korea's latest missile launch
* Euro net long positions rise to highest in over 3 years-IMM
* Sterling edges up but seen pressured by latest polls
* S Africa's rand jumps after Zuma defeats no-confidence motion
TOKYO, May 29 (Reuters) - The dollar was steady in early Asian trading on Monday, holding well above last week's 6-1/2-month lows and taking news of Pyongyang's latest missile test in stride.
The dollar index, which tracks the U.S. currency against a basket of six major rivals, was flat at 97.432, some distance from last week's low of 96.797, its weakest since Nov. 9.
The greenback edged down slightly to 111.23 yen but mostly held 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. markets closed on Monday for the Memorial Day holiday, major currency pairs were likely to tread water, with no incentive 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 communications with Moscow before Trump took office.
The euro was steady on the day at $1.1173, 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 risks 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 $1.2811 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 British Prime Minister Theresa May's lead over the opposition Labour Party has narrowed sharply since last week's terror attack in Manchester, suggesting she might not win 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 initially 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 Africa President Jacob Zuma defeated a no-confidence motion against him at a meeting of top officials of the ruling African National Congress party on Sunday.
The greenback was last down 0.5 percent at 12.7925 rand. (Reporting by Tokyo markets team; Editing by Shri Navaratnam)