Britain on Tuesday set a hard deadline of December 2020 to reach a new trade deal with the EU, trying to pressure Brussels to move more quickly to seal an accord.
Johnson will use his control of parliament to outlaw any extention of the Brexit transition period beyond 2020.
It was his boldest move since winning a large majority in last Thursday's election, and it spooked financial markets.
The pound had fallen 1.23pc to $1.317 in North American trade, and was down 2.55pc from Friday when it hit its highest since May 2018 in the wake of Johnson's electoral victory.
"Sterling-negative Brexit uncertainty returned to the forefront," said Joe Manimbo, senior market analyst at Western Union Business Solutions.
The euro rose against the pound, last up 1.36pc to trade at 0.847 pence, its strength bolstering it against the U.S. dollar as well.
"The move appears to be the knee-jerk variety for the euro as Brexit uncertainty would only complicate Europe's already challenging economic backdrop. A better test of euro sentiment arrives Wednesday with the final reading of euro zone inflation for November which is forecast to go unrevised at a low 1pc, compared to the ECB's near 2pc bullseye," said Manimbo.
The dollar index was slightly higher, up 0.13pc to 97.147, driven by the fall in the pound as well as a fall in the Australian dollar.
The Aussie fell to a weekly low on Tuesday after the central bank opened the door to another cut in interest rates as early as February.
The trade-linked currency also weakened as euphoria from the U.S.-China trade agreement faded. It was last down 0.51pc at 0.685 U.S. dollars to the Aussie.
The "phase one" trade deal between Washington and Beijing, announced on Friday after more than 2-1/2 years of volatile negotiations, will reduce U.S. tariffs on Chinese goods in exchange for increased Chinese purchases of some U.S. goods.
Fitch ratings agency said the deal eased U.S.-China tensions but that renewed escalation remains a significant risk, with the issue of technology posing an obstacle to full resolution.