By David Lawder and Andrea Shalal

WASHINGTON (Reuters) - U.S. President Donald Trump on Saturday ordered a new trade investigation that could heap more tariffs on imported lumber, adding to existing duties on Canadian softwood lumber and 25% tariffs on all Canadian and Mexican goods due next week.

In his third new tariff probe in a week, Trump signed a memo ordering Commerce Secretary Howard Lutnick to initiate a national security investigation into U.S. lumber imports under Section 232 of the Trade Expansion Act of 1962. The trade law is the one Trump also used to impose tariffs on global steel and aluminum imports.

The probe covers derivative products made from lumber which could include furniture such as kitchen cabinets, which in some cases are made of U.S. lumber that had been exported, a White House official said.

The official said the investigation would be expedited by the Commerce Department, but gave no specific timeline.Trump also ordered new steps to increase the domestic supply of lumber by streamlining the permitting process for harvesting lumber from public lands and improving the salvage of fallen trees from forests and waterways, the official said.

A White House fact sheet said the order calls for new or updated agency guidance to facilitate increased timber production, including quicker approvals for forestry projects under the Endangered Species Act.

White House trade adviser Peter Navarro said the lumber import probe would counteract the actions of big lumber exporters including Canada, Germany and Brazil, which he said were "dumping lumber into our markets at the expense of both our economic prosperity and national security."

"That stops today with a pair of Trumpian actions designed to both bolster supply of and demand for American timber and lumber," he told reporters on a conference call ahead of the signing.

The White House official said that increasing reliance on imported lumber represents a possible national security risk partly because the U.S. military consumes significant quantities of lumber for its construction activities and because increasing dependence on imports for a commodity with ample domestic supplies is a danger to the U.S. economy.

The official did not provide details on a proposed tariff rate under the Section 232 lumber probe, but Trump earlier this month told reporters that he was thinking about imposing a 25% tariff rate on lumber and forest products.

The official said any tariffs resulting from the probe would be added to the existing 14.5% combined anti-dumping and anti-subsidy duties on Canadian softwood lumber.

These were the result of a long-running U.S.-Canada trade dispute over Canada's low stumpage fees on public lands, which Washington argues is an unfair subsidy. Most U.S. lumber is harvested from private land at market-determined rates. Home builders have long criticized the tariffs as raising lumber prices and contributing to home price inflation.

The official said the new lumber duties also would stack on top of Trump's threatened 25% general U.S. tariffs on all Canadian and Mexican goods that are scheduled to take effect on Tuesday unless Trump is persuaded by the two countries' efforts to secure their borders and halt fentanyl trafficking.

The new tariff probe follows Trump's order on Tuesday for a new Section 232 into copper imports, aimed at rebuilding U.S. production of a metal critical to electric vehicles, military hardware and the power grid.

On Feb. 21, Trump ordered U.S. Trade Representative Jamieson Greer to revive investigations aimed at imposing tariffs on imports from countries that levy digital services taxes on U.S. technology companies. Canada would again be in the firing line for such penalties, along with France, Britain, Italy, Spain, Austria, India and Turkey.

(Reporting by David Lawder and Andrea Shalal; additional reporting by Trevor Hunnicutt and David Shepardson; Editing by Chizu Nomiyama)