The White House says there could be exemptions to US plans to impose tariffs on metal imports, in a softening of its tough stance.
Canada, Mexico and other countries may see "carve-outs" on national security grounds, press secretary Sarah Sanders said.
US President Donald Trump has said steel products will face a 25 per cent tariff, with 10 per cent on aluminium goods.
But there are fears the plans could spark a trade war.
The EU has proposed retaliatory measures against a number of US goods including bourbon and peanut butter.
Despite opposition at home and abroad, Ms Sanders said the US president would sign the measures by the end of the week, with US media reporting it could happen as early as Thursday.
But she added: "There are potential carve-outs for Mexico and Canada based on national security, and possibly other countries as well based on that process. That would be [on] a case-by-case and country by country basis."
Mr Trump has railed against the US trade deficit, arguing that other countries have been "taking advantage of" the US for decades.
One of his campaign promises was to rebuild the US steel and aluminium industries which he said has suffered "disgraceful" treatment from other countries, in particular cheap Chinese imports.
Last week he dismissed concerns he could trigger a trade war, instead saying "trade wars are good" and were something the US would easily win.
Mr Trump has already hinted he could drop plans to impose tariffs on Mexican and Canadian metals but linked it to the US getting a better deal in the North American Free Trade Agreement.
Mexico and Canada are among the main suppliers of steel to the US.
The US plans have sparked worldwide alarm and jolted stock markets.
Critics argue that the tariffs would fail to protect American jobs and would ultimately raise prices for consumers.
According to BBC, International Monetary Fund chief Christine Lagarde warned "nobody wins" in a trade war, saying it would harm global economic growth.
The EU has set out tit-for-tat plans to impose import duties on bourbon, peanut butter, cranberries, orange juice, steel, and industrial products. Other countries, including China, are also considering retaliatory steps.
Members of Mr Trump's Republican party are concerned too, with House Speaker Paul Ryan saying he wanted to see tariffs that were "more surgical and more targeted".
Tuesday saw the departure of top White House economic advisor Gary Cohn, who is a strong supporter of free trade.