Updates prices at 1215 GMT

By Alun John and Kevin Buckland

LONDON/TOKYO, July 2 (Reuters) -European stocks dipped on Tuesday, reversing some of the previous day's relief rally, while the U.S. dollar hit a near 38-year high versus the Japanese yen as the possibility of a second Donald Trump presidency left Treasury yields elevated.

Europe's broad Stoxx 600 .STOXX share index shed 0.8% and France's CAC40 .FCHI dropped a similar amount, unable to hold onto its gains from the day before. Most other European national indexes, including in Britain .FTSE, Germany .GDAXI Italy .FTMIB and Spain .IBEX, were also in the red. .EU

The French blue-chip benchmark rose 1% on Monday as the first round of voting in the country's parliamentary election indicated the most likely eventual outcome would be legislative gridlock rather than a majority for the far right or left.

The premium that investors require to hold French debt over German also narrowed after the result and was last at 75 basis points, though investors remain wary ahead of a second and final round of voting this coming Sunday. DE10FR10=RR

Tuesday's focus is on whether opponents of France's far right can build a united front to hinder its path to victory.

"The economic backdrop remains favourable for Europe, but political risk is back - in France - and proving impactful," said Samy Chaar, chief economist at Lombard Odier.

Euro zone consumer inflation, released on Tuesday, came in at 2.5%, in line with expectations.

Elections are also on investors' minds when it comes to U.S. assets, with Treasury yields remaining elevated and supportive of the dollar.

"It certainly looks to us to be investors increasingly trading on the prospect of a Trump victory. More fiscal stimulus and trade tariffs (are) ... inflationary and could be putting upside pressure on longer-term yields," said Derek Halpenny, head of research, global markets EMEA at MUFG.

"The Constitutional Court decision yesterday that a president is immune from prosecution when carrying out his/her 'official' duties is another development that will increase expectations of a Trump victory on 5th November."

The benchmark 10-year Treasury yield was last at 4.45%, down 3 basis points on the day, but in sight of the previous day's one-month high of 4.49%, and up around 20 basis points in less than a week. US10YT=RR US/

Germany's 10-year yield DE10YT=RR was last at 2.61%, a near three-week high, moving alongside its U.S. peer, and also having risen as investors unwound some of their flight to safe haven assets after the French election. GVD/EUR

U.S. S&P 500 and Nasdaq futures were around 0.5% lower. ESc1, NQcv1

YEN WATCHING

The higher U.S. yields supported the dollar, and the euro was down 0.1% at $1.0729. EUR=EBS

The dollar's moves against the Japanese yen were more striking and it rose as high as 161.745 yen JPY=EBS on Tuesday, a level not seen since December 1986, leaving traders on high alert for Japanese intervention.

Japanese authorities spent some 9.8 trillion yen ($60.65 billion) to support the beleaguered currency when it plunged to 160.82 per dollar in the days spanning late April and early May. While it has since weakened past that level, the pace of change has been less dramatic than in late April.

Japanese Finance Minister Shunichi Suzuki reiterated on Tuesday that officials were watching currency markets with vigilance, but he noticeably did not repeat a warning that they stood ready to act.

Japan's Nikkei share index, which often, but not always, benefits from a weaker currency, rallied more than 1%, putting it head and shoulders above other major markets in the region. .T .N225

Monetary policy will be in focus later in the day, when Federal Reserve Chair Jerome Powell and other top policy makers speak at an event in Sintra, Portugal, hosted by the European Central Bank.

A parade of potentially crucial U.S. employment data also begins on Tuesday with the JOLTS job openings report, a Fed favourite, followed by ADP numbers a day later and the all-important monthly payrolls figures on Friday.

In energy markets, Brent LCOc1 futures added 0.8% to $87.28 per barrel, building on a 1.9% overnight rally on possible supply disruptions from Hurricane Beryl. O/R

Gold was down 0.5% at $2320.7 an ounce. GOL/

($1 = 161.5900 yen)

Reporting by Alun John and Kevin Buckland; Editing by Gareth Jones and David Holmes

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