* Data shows continued weakness in inflation
* North Korean tensions keep demand for bonds
* Friday's employment report in focus
NEW YORK, Aug 31 (Reuters) - U.S. Treasury prices gained slightly on Thursday after consumer spending data showed continuing low inflation, and as tensions with North Korea kept up demand for the safe haven bonds.
U.S. consumer spending rose slightly less than expected in July and annual inflation increased at its slowest pace since late 2015.
The personal consumption expenditures (PCE) price index excluding food and energy edged up 0.1 percent in July. In the 12 months through July, the core PCE price index increased 1.4 percent, the smallest year-on-year increase since December 2015.
After a run of low numbers, and given that June was the last one that didnt disappoint to the downside, there were people thinking maybe we will get a small upside surprise, but not this time, said Jim Vogel, an interest rate strategist at FTN Financial in Memphis, Tennessee.
Benchmark 10-year notes were last up 2/32 in price to yield 2.138 percent, down from 2.145 percent on Wednesday.
Other data showed that the number of Americans filing for unemployment benefits rose slightly last week.
Escalated tensions between the U.S. and North Korea also boosted demand for Treasuries.
South Korean and Japanese jets joined exercises with two U.S. nuclear-capable bombers above and near the Korean peninsula on Thursday, two days after North Korea fired a missile over Japan.
Trading volumes were relatively low, however, with some investors reluctant to buy Treasuries given that yields are near their lowest levels since November.
People have been nervous about the levels for the last two weeks, which is one of the reasons youve seen volume really fall back, said Vogel.
Fridays employment report for August is the next major economic focus. Employers are expected to have added 180,000 jobs in the month, according to the median estimate of 93 economists polled by Reuters.
Central bank meetings next month are also in focus, with the European Central Bank under the most scrutiny for any indications that it is near a decision to pare its asset purchases.
Rapid gains by the euro against the dollar are worrying a growing number of policymakers at the ECB, raising the chance its asset purchases will be phased out only slowly, three sources familiar with discussions told Reuters. (Editing by Chizu Nomiyama) )