BlackRock's global fixed income chief says the European Central Bank just turned up the pressure on the Federal Reserve, making it slightly more possible the Fed could cut rates Wednesday instead of waiting to do so in July as expected.

Rick Rieder, who is also head portfolio manager for BlackRock's Global Allocation Fund, does not expect a Fed rate cut until July, but he said the European Central Bank head's dovish comments signal the ECB is going to ease its policy even more.

"I do think there is a chance they go, but the odds are not high," Rieder said of a possible Fed move Wednesday.

ECB President Mario Draghi said Tuesday that Europe's central bank could cut interest rates again or conduct more asset purchases if inflation doesn't meet its target. That sent global bond yields tumbling, with the German 10-year bund yield falling to an all-time low of negative 0.32% and the French 10-year to its first negative yield ever.

"I think Draghi raised the bar. I think Draghi, his comments here are very aggressive. When he says inflation has to be above that level at some time in the future, that doesn't hit the bar, that says he wants to go beyond it. That raises the bar," said Rieder. The ECB has been aiming to keep inflation close to 2%, well above the May level of about 1.2% for the euro zone.

Rieder, whose firm manages $6.5 trillion in investments and is the world's largest asset manager, said Draghi is also putting his mark on policy that could remain in place after he steps aside in October. "I do think of this as his legacy statement. He is setting a framework out there so whoever the incoming president is going to consider this very highly and not reverse course. He's putting a stake in the ground."

As the European yields fell to record lows Tuesday, the U.S. 10-year yield reached 2.01%, its lowest level since 2016. The yield, which moves opposite price, rose to 2.05% later in the day. "I do think we're going to get below a 2% 10-year," Rieder said. "It has to do with trade. I do think the U.S. economy is in good shape, and I think ultimately rates can trend higher. I think you can get another 30, 40 basis points higher in yield The next steps are going to be a bit lower."

Rieder said if the trade situation between the U.S. and China deteriorated, the 10-year yield could fall to 1.8 or 1.85%.