President Donald Trump has refused to back down from imposing his planned tariffs on steel and aluminium imports into the US despite pleas from his own party.

Trump has been unmoved by lobbying from lawmakers, leading companies and industry groups since he first announced the measure. If anything, he has repeatedly upped the ante.

"We're not backing down," Trump said during a White House meeting with Israeli Prime Minister Benjamin Netanyahu on Monday. "I don't think you're going to have a trade war," he added, without elaborating.

At the same time, he has increased pressure on Canada and Mexico over trade, saying the two could avoid being caught in his planned hefty tariffs if they ceded ground in talks on a new NAFTA trade deal.

Trump's determination to push ahead with a 25 per cent tariff on steel imports and a 10 per cent duty on aluminium has prompted threats of retaliation from the European Union, Canada, China and Brazil among others. It has roiled world stockmarkets as investors worry about the prospect for an ever-escalating trade war that would derail global economic growth.

His plan, announced on Thursday, has also hit resistance from some senior figures in his own Republican Party.

House of Representatives Speaker Paul Ryan, a Republican whose state of Wisconsin would be hit by proposed European counter-tariffs on Harley Davidson motorcycles, urged the White House on Monday not to push ahead with the action.

Trump's tariff plan is "the most irrational economic policy that any President has ever introduced in the last half century," says the former U.S. Treasury Secretary.

Fellow Republican Kevin Brady, the top House legislator on trade, said American consumers should not be forced to pay more for goods.

Trump was expected to finalise the planned tariffs later in the week, posing a tough challenge for US Trade Representative Robert Lighthizer, Canada's Foreign Minister Chrystia Freeland and Mexican Economy Minister Ildefonso Guajardo. They were meeting in Mexico City on Monday to wrap up the latest round of discussions on revamping the 1994 NAFTA deal.

Trump has touted the tariffs as a way to revive the US steel and aluminium industries, in keeping with his promises both on the campaign trail and in the White House that he will seek deals that better favour American workers.

That has included the threat that Washington will withdraw from NAFTA if it is not satisfactorily renegotiated.

In Washington, aides scrambled to meet Trump's demand for the paperwork to be completed for a formal announcement this week. The exact timing was still unclear as the tariff documentation had to be drafted and go through a variety of reviews, a process that takes days, an administration official said.

Trump remained adamant about signing the tariffs, according to officials in and out of the White House. The president "sees this as a base issue for him", one Trump outside adviser said.