Near 10:13 a.m. ET, the Dow was up 95 points, the S&P 500 was up 8 points, and the Nasdaq was up 29 points.
Bond yields, which rise when their prices fall, are spiking.
The yield on the benchmark 10-year German bund jumped as much as 12 basis points to around 0.82%, the highest level since last November.
US government bond yields are higher across all durations; the benchmark 10-year note rose by up to 7 basis points to 2.33%, its highs of the year.
Markets were fixated on the European Central Bank's Mario Draghi, as he gave a press conference following the latest monetary policy decision that left rates unchanged. Business Insider's Myles Udland has the full wrap of his remarks.
In economic data, ADP private payrolls grew by 201,000 in May, just slightly better than expected.
The trade deficit narrowed by 19% to $40.9 billion in April - more than expected. Economists had estimated that the deficit - the excess of imports over exports - fell to $-44 billion.
And, the services sector slowed down in May. Markit's Purchasing Managers' Index came in lower than expected, at 56.2, while ISM's non-manufacturing index fell to 55.7, the lowest reading since April 2014.
Data on US oil inventories is also due this morning.
Investing.com
German 10-year bund yield