Draghi expressed his view on these issues at his news conference after a central bank policy meeting. It overshadowed the ECB's dropping of a long-standing pledge to increase its bond purchases if needed, a move that briefly spurred buying of the single currency.
"All of which sent the euro yo-yoing as the markets ponder the very real threat of a trade war between the U.S. and the EU," said David Lamb, head of dealing at FEXCO Corporate Payments in Edinburgh.
Draghi's comment on protectionism came as traders awaited details on U.S. President Donald Trump's proposed tariffs on imported steel and aluminum, which has whipped up anxiety about a global trade war.
Trump was expected to sign a proclamation later Thursday or on Friday to impose a 25 percent levy on steel and a 10 percent tariff on aluminum. Trump promised earlier on Thursday to show great flexibility and cooperation toward the United States' "real friends" after a White House official said late on Wednesday that Trump was considering offering Canada and Mexico a 30-day exemption from the tariffs.
The dollar, which is seen a safe haven on trade war fears, had dipped on prospects for a softening stance on the tariffs before gaining on perceived dovish remarks from Draghi. The greenback had weakened following the resignation on Tuesday of Gary Cohn, Trump's top economic adviser, who was seen as a bulwark against protectionism in the White House.
The index, which tracks the greenback versus a basket of six currencies, rose 0.58 percent, to 90.15.
The euro was last down 0.85 percent at $1.2307. With the ECB in the rear-view mirror, traders await news from the Bank of Japan's policy meeting and the U.S. government's payrolls report for February.
"We think that they will not make any changes. Inflation is ticking higher but under their target," said John Doyle, vice president of dealing and trading at Tempus Inc in Washington.
On Tuesday, Bank of Japan Governor Haruhiko Kuroda said a future exit of its ultra-loose monetary policy would need to be "very gradual," tempering his remarks before lawmakers that the central bank would consider an exit if his inflation target were reached in fiscal 2019.
The dollar was last up 0.12 percent, at 106.19 yen.