* Asian stocks up slightly, near 2-year high
U.S. bond yields at 1 1/2-month highs
* Qatari shares at 1 1/2-year lows
By Hideyuki Sano
TOKYO, July 3 (Reuters) - Asian stocks held two-years highs on Monday, starting the new month on a solid footing after two quarters of gains while expectations of credit tightening by the world's central banks kept global bond markets under pressure.
MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.1 percent, staying within a stone's throw of its two-year peak hit last week.
Japan's Nikkei ticked up 0.2 percent while U.S. stock futures gained 0.2 percent.
"Global share markets have so far withstood rises in long-term bond yields," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
Signs of stabilising in China's economy and a recovery in the European economy helped to boost global share prices in the first half of this year.
Against this backdrop, on Wall Street, the S&P 500 scored its biggest gain for the first half of the year since 2013 while the Nasdaq Composite's first-half gain was its best in eight years.
Signs of steady economic recovery, however, have prompted some of the world's central banks to drop hints that their monetary policies could be tightened in coming months.
Global bond yields have risen sharply following comments from European Central Bank President Mario Draghi last Tuesday, with German bond yields posting their biggest weekly jump since December 2015 last week.
That helped to lift U.S. bond yields from lows, with the 10-year U.S. Treasuries yield hitting a 1 1/2-month high of 2.320 percent on Monday.
The rise came even as data showed U.S. inflation cooled in May. The annual rise in core consumer prices excluding food and energy slowed to 1.4 percent, its lowest since December 2015.
"In coming weeks, whether we can see a recovery in the U.S. momentum will be a key issue," said Hirokazu Kabeya, chief global strategist at Daiwa Securities.
In the currency market, the euro traded at $1.1423, not far from last week's high of $1.1445, which was its highest level in more than a year as the common currency drew support from expectations that the ECB will likely scale back its stimulus.
The dollar traded at 112.30 yen, off Thursday's six-week high of 112.93.
The yen briefly gained on worries Japanese Prime Minister Shinzo Abe's reflationary policies may be at risk after his Liberal Democratic Party suffered an historic defeat in a local election in Tokyo on Sunday, though the impact did not last long.
The Bank of Japan's tankan corporate survey showed Japanese business sentiment improved slightly more than expected though there was no market reaction.
Oil prices held firm after having gained for seven consecutive sessions by Friday, drawing support from a decrease in the U.S. rig count and stronger demand data from China.
Brent crude futures rose 0.3 percent to $48.90 per barrel while U.S. crude futures gained 0.5 percent to $46.26 per barrel.
In the Middle East, Qatari shares slumped to 1 1/2-year lows on Sunday as a deadline for Doha to accept a series of political demands by four Arab states was expected to expire late in the day with no sign of the crisis ending.
Saudi Arabia and three allies accusing Qatar of supporting terrorism have agreed to a request by Kuwait to extend by 48 hours Sunday's deadline for Doha to comply, according to a joint statement on Saudi state news agency SPA.
(Editing by Sam Holmes)