Analysts said concerns that coronavirus will hurt the world economy, alongside political uncertainty in Germany, continued to underpin bond markets.
But for now further falls in bond yields, and price rises, were difficult in the face of rallying equity markets. Asian share markets followed Wall Street up on Tuesday, while European stocks opened broadly higher.
"The story this morning is that the risk recovery in Asian markets is questioning the low yield levels we saw yesterday -- Bund yields at -0.40pc are hard to defend when stocks are doing well," said Commerzbank rates strategist Christoph Rieger.
"Having said that, at these levels, EGBs (European government bonds) are very resilient given the lingering uncertainty, aided by uncertainty in Germany as well."
Annegret Kramp-Karrenbauer, the woman who had been expected to become Germany's next chancellor, said on Monday she would not run for the top job -- succumbing to a scandal involving the far right and blowing open the race to succeed Angela Merkel.
In early trade, most 10-year bond yields were 1 to 2 basis points higher on the day.
Germany's benchmark Bund yield was up 1.6 bps at -0.398pc , not far off a low of -0.41pc hit on Monday.
It is down around 20 bps so far this year on concern that the coronavirus outbreak will hurt economic growth and encourage the European Central Bank to maintain an easy monetary policy stance.
ECB Presudebt Christine Lagarde is scheduled to speak later this session, while U.S. Federal Reserve Chairman Jerome Powell will deliver a semi-annual testimony to Congress.
The text of Powell's testimony was published on Friday, so focus was expected to fall on the question-and-answer session.
"Mentions of a symmetric target will likely be taken dovishly, as will indications that downside risks (most probably due to the virus) are more significant than initially thought," analysts at Mizuho said in a note.
Elsewhere, Italy was expected to issue a new 15-year bond via a syndicate of banks.