TOKYO, July 4 (Reuters) - Japanese government bond prices firmed on Monday following solid gains in their U.S. counterparts late last week, with two-, five- and 20-year yields hitting record lows before the market gave up gains ahead of a 10-year JGB auction later this week.

The 20-year JGB yield fell to as low as 0.035 percent , before stepping back to 0.045 percent, up 0.5 of a basis point from Friday.

The five-year yield fell to a record low of minus 0.375 percent while the two-year yield dipped to minus 0.340 percent.

The 10-year yield fell to minus 0.260 percent , matching a record low touched last week, before bouncing back to minus 0.255 percent ahead of Tuesday's 10-year JGB auction.

The market was supported by a fall in U.S. Treasury yields on Friday, amid a worldwide scramble for bonds on expectations of weak global growth and more policy stimulus from major central banks. The 30-year U.S. yield hit its lowest since the 1950s.

The Japanese bond market is also helped by expectations that the Bank of Japan is likely to adopt monetary easing at its policy meeting at the end of this month.

The one-year overnight indexed swap (OIS) rate hit minus 0.252 percent, its lowest level since late April, compared to the current overnight rate around minus 0.06 percent.

(Reporting by Tokyo Markets Team; Editing by Sam Holmes)