EU bond yields collapsed, after ECB President Christine Lagarde said the central bank is closely monitoring the rise in borrowing costs.

According to latest reports, borrowing costs in Europe rose sharply this month, as prospects for stronger US fiscal stimulus raised hopes for a faster global economic recovery.

Lagarde's comments indicating that policymakers in Europe are uncomfortable with the recent surge in earnings have led to lower yields.

"The ECB cannot afford an increase in nominal or real yields without inflation, because higher yields are tightening the economic conditions for the bloc," said Althea Spinozzi, strategist at Saxo Bank.

"The ECB will do everything to control the yields of European sovereign bonds," she added.

Germany's 10-year bond yields fell 3.5 basis points to -0.34%, the biggest daily fall since mid-December. In the morning, they hit a new eight-month high, after rising nearly 12 basis points last week, which is the biggest weekly jump since June.

As for the US, bond yields increased by up to 20 basis points, a sign that indicates that sell-off in the Treasury bond markets is widening.

"This is a key change because it calls into question the veracity of the Fed's promise to tolerate excess inflation in the future," said Gilles Moek, chief economist at AXA.

"It is clear why the yield on US Treasuries is growing and is expected to grow," said Chris Scicluna, economist at Daiwa Capital Markets. "Fiscal support in the US, as well as increasing pace of vaccination, points to a stronger economic recovery and higher inflation, even if it is temporary," he added.

Perhaps, a more worrisome sign for policymakers is that real inflation-adjusted bond yields have jumped sharply over the past week. The inflation-related yield on Germany's 10-year bonds rose to -1.28% on Monday, the highest since October last year.

Meanwhile, Italy's 10-year bond yields fell by 2.5 basis points.

The recent sell-off has increased the steepness of the yield curve in Germany, with the gap between 2-year and 10-year yields being the largest in nearly a year.

And according to Lagarde, since about € 1 trillion is still not spent on the Emergency Procurement Procedures (EPP) due to the pandemic, the ECB still has leverage to manage financing terms.

The ECB has long argued that even if the procurement quota is exhausted, politicians will still be able to get out of their biggest crisis.

Lagarde also reiterated the ECB's pledge to maintain favorable funding to help the people and the economy during the pandemic.