* World stocks rise for third straight session
* Silver prices head for best quarter in four years
* GRAPHIC-2016 asset returns: http://reut.rs/1WAiOSC
* GRAPHIC-Gold/silver ratio: http://link.reuters.com/kuq35s (Updates prices; adds comment, second byline, NEW YORK dateline)
By Marcy Nicholson and Jan Harvey
NEW YORK/LONDON, June 30 (Reuters) - Gold steadied on Thursday as the other markets showed signs of stabilizing, but remained on track for its biggest monthly rise since February in the wake of last week's vote in Britain to quit the European Union.
Shares, bonds and currencies plunged on Friday after the British referendum sent investors scurrying for the perceived safety of gold, which leapt to its highest in nearly two years at $1,358.20 an ounce.
But the immediate market flurry over the vote settled on Thursday, with world stock markets rising for a third day and bond yields hovering around record lows. MKTS/GLOB
Bank of England Governor Mark Carney said the central bank would probably need to pump more stimulus into Britain's economy over the summer. gold XAU= was up 0.2 percent at $1,320.90 an ounce at 3:31 p.m. EDT (1931 GMT), while U.S. gold futures GCv1 for August delivery settled down 0.5 percent at $1,320.60.
"For the market, there's more to digest and that means you're not really seeing more long accumulation or capitulation," said Rob Haworth, senior investment strategist for U.S. Bank Wealth Management in Seattle.
"We're all waiting for political news out of the U.K."
Profit taking and a lack of physical demand is keeping gold hemmed in, said Afshin Nabavi, head of trading at MKS.
Holdings of the world's largest gold-backed exchange-traded fund, New York-listed SPDR Gold Shares GLD , have increased by 131 tonnes this quarter, a second consecutive quarterly inflow for the first time since late 2012.
Gold remains up 8.7 percent this month, and is on track for a second straight quarterly gain and a rise of 24.4 percent for the first half of the year.
Silver is heading for its best quarter in nearly four years, up about 22 percent.
Silver XAG= was 2.7 percent higher at $18.76 an ounce, having hit $18.80, the highest since September 2014.
The gold-silver ratio, which measures the number of silver ounces needed to buy an ounce of gold, fell to its lowest in 13 months at 70.4.
"Silver is clearly profiting from two different sides at once just now: from the higher gold price on the one hand and from firm base metal prices on the other, as silver is used for the most part in industry," Commerzbank (DE:CBKG) said in a note.
Platinum XPT= was up 2.3 percent at $1,025.60 an ounce, after rising to $1,026.10, the highest since May 20. Palladium XPD= was up 1.7 percent at $595.47, after reaching $598.26, the highest since May 13.
<^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ GRAPHIC-2016 asset returns:
http://reut.rs/1WAiOSC GRAPHIC-Gold/silver ratio:
http://link.reuters.com/kuq35s
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^> (Additional reporting By Nallur Sethuraman and Vijaykumar Vedala in Bengaluru; Editing by Mark Potter and Chizu Nomiyama)