The dollar pushed to a new 11-year high against the euro on Friday, after a strong U.S. jobs report solidified market expectations for the Federal Reserve to raise interest rates around midyear.

The euro fell to $1.0839 in late-afternoon trading in New York, its lowest level against the dollar since Sept. 4, 2003. The euro recovered slightly to end the session down 1.7% at $1.0843 in its largest one-day decline in six weeks.

The...