* Dollar climbs off lows versus euro, yen ahead of US jobs report

* Trump election risk to cut short any dollar gains on jobs report

* Sterling stands tall after rallying on High Court Brexit ruling

* Kiwi near 1-mth high, helped by higher milk prices & upbeat data (Updates prices, adds details and quotes)

By Shinichi Saoshiro

TOKYO, Nov 4 (Reuters) - The dollar clawed back some ground against its major peers on Friday ahead of the U.S. non-farm payrolls report later in the day, but remained captive to jitters over a tightening U.S. presidential election race.

The dollar index edged up 0.1 percent to 97.244, pulling away from a three-week low of 97.041 seen overnight.

The index had hit a nine-month high above 99.00 last week on enhanced prospects of the Federal Reserve hiking interest rates later this year.

But it was on track to fall about 1.2 percent this week as Democrat Hillary Clinton's lead over Republican Donald Trump in the polls has appeared to dwindle following the re-emergence of a controversy over her private email server.

Clinton is viewed as a candidate of the status quo, while there is much more uncertainty over Trump's stance on key issues including foreign policy, trade and the economy.

"Participants are not responding very much to reports that suggest Clinton is ahead in some battleground states. Emotions has the edge over logic right now," said Masashi Murata, senior currency strategist at Brown Brothers Harriman in Tokyo.

"Fundamentally, nothing has changed since mid-October, when the dollar was rising steadily."

The currency market has focused on the Nov. 8 election and having paid scant attention to key events like the Fed's policy decision earlier in the week. But the U.S. non-farm payrolls report later on Friday could impact expectations of a December Fed rate hike.

"The market is likely to greet a strong payrolls report with a straight forward enough response and bid the dollar higher. But the rise could fade quickly amid the 'Trump risk' woes," said Junichi Ishikawa, senior FX strategist at IG Securities in Tokyo.

Any rise in the dollar right now will provide an opportunity for participants who have been caught long on the dollar and want to square their positions, Ishikawa said.

Economists polled by Reuters are looking for non-farm employment to have risen by 175,000 in October from 156,000 in September.

An upbeat jobs report is expected to increase hopes for a December U.S. interest rate hike, which usually pushes U.S. yields higher and supports the greenback.

The dollar inched up 0.1 percent to 103.080 yen, having clawed higher from a one-month low of 102.55 struck overnight.

It has fallen 1.6 percent this week from well above 105.00 as polls showed Trump was closing the gap with Clinton and even pulling slightly ahead in a few states.

The yen, along with other perceived safe-havens like the Swiss franc, has benefited this week as Trump risk jitters have created a risk off mood in the global markets.

The euro was down 0.1 percent at $1.1092, having pulled back from a three-week high of $1.1126 touched the previous day. It was en route for a 1 percent weekly gain.

Sterling nudged up 0.1 percent to $1.2476 after rallying more than 1 percent overnight to a four-week peak.

The pound surged on Thursday after the country's High Court ruled that the government needed parliamentary approval to trigger procedures to leave the European Union, easing Brexit fears for the time being.

The Australian dollar was little changed at $0.7679 , on track to rise 1.2 percent this week. The Aussie was boosted earlier this week after the country's central bank kept steady on monetary policy and provided no easing bias.

The New Zealand dollar hovered near a one-month high of $0.7342 struck on Thursday, supported this week by a rise in international milk prices and strong local employment data.

(Editing by Kim Coghill)