Bund futures fell 10 ticks to 146.24 shortly after the open, but remained at extremely elevated levels after hitting a record high of 146.89 on Friday. Last week, the contract rallied 227 ticks.
Analysts said the flight to safe-haven bonds was expected to continue until clarity emerged on issues such as the outcome of Greek elections due on June 17 and the recapitalisation of European banks, now exposed to a crisis in Spain.
"Markets have moved to extremes and mounting global macro worries have joined the anxiety about Spain and Greece. Bunds and (US) Treasuries will remain bid as risk assets are hammered," said Commerzbank strategist Rainer Guntermann in a note to clients.
Selling of riskier assets such as equities accelerated in Asian trading as concerns about the health of the US economy gathered pace after a non-farm payrolls report on Friday showed the US economy added far fewer jobs in May than expected.
In the euro zone, German Chancellor Angela Merkel responded to the bloc's deepening crisis by pressing for closer integration, including a central authority to manage finances and sweeping new powers for Europe's political and legal institutions.
However, the long-term plans were not expected to offer much relief for investors fretting over the possibility of a Greek exit from the currency union and the mounting problems in Spain that may require some form of bailout.