Those who did join Trump said he appeared open-minded, seeking solutions from everyone - including executives from the video-game industry.
In Asia, a large share of Japanese and Chinese steel goes to countries in the region's southeast, where booming construction and light industries are fueling strong demand for steel. "If you care about this issue, you will look at Jonesboro, Arkansas; Columbine; Newton, Connecticut", said Bozell.
Other countries can apply for exemptions, according to the administration, although details of when they would be granted were thin.
Trump announced Thursday that he was slapping tariffs of 25 percent on imported steel and 10 percent on aluminum, but he temporarily exempted big steel producers Canada and Mexico - provided they agree to renegotiate a North American trade deal to his satisfaction.
"These days the markets trade hundreds of points each way based on what the president tweets and I am surprised that the markets have been as benign as they have been in the wake of this news", said one investor, who declined to be named.
Trump has been openly critical of the state's political leaders and policies.
The EU has warned that it stands ready to slap "rebalancing" tariffs on about 2.8 billion euros ($3.4 billion) worth of US steel, agricultural and other products, like peanut butter, cranberries and orange juice.
The Chinese government said it "firmly opposes" the move but gave no indication whether it might make good on threats to retaliate.
Mr Turnbull welcomed the way Mr Trump had recognised that Australia was a strong ally of the USA and that America has a large trade surplus with Australia.
In the U.S., Gary Shapiro, president and CEO of the Consumer Technology Association, which represents more than 2,200 companies, said the tariffs could cost far more American jobs than they would create. Whether the pursuit of measures to stem imports of steel and aluminum were originally seen as part and parcel of the NAFTA renegotiations or whether this is an opportunistic melding of otherwise completely separate issues is hard to tell. The first instituted global tariffs of 24 percent on steel and 7.7 percent on aluminum-with no exemptions. That would risk Australian jobs.
"The idea that jurisdictions where they're now making steel and aluminium, the idea that if they can't ship it to America they'll just sit at home and do nothing, that is negligent attitude", he said.
"We're going to be very fair, we're going to be very flexible but we're going to protect the American worker as I said I would do in my campaign", Trump said during a Cabinet meeting.
"We've got to make sure the penalties are in place so that everyone dealing with Australia, plays by the rules".
The chief USA negotiator for autos returned to Washington after one day in Mexico City, effectively placing on hold any exchange of details on rules of origin, the sources said.
NPR's Philip Reeve tells Morning Edition that Brazil is gravely concerned about the US tariffs, saying they will hurt trade relations and that the South American country has not ruled out sourcing its coal from elsewhere. Mr Trump took to Twitter on Saturday morning to say he'd spoken with the prime minister.
Malmstrom warned the Trump administration against considering metal-tariff exemptions for only some European Union countries such as the United Kingdom, which, while long considering that it has a special relationship with the US, she said is behind the bloc on the issue.