UPDATE 1-Trump to demand G20 take stronger action on steel overcapacity -adviser

-adviser@ (Adds details on steel probe, quotes on trade)

WASHINGTON, June 29 (Reuters) - U.S. President Donald Trump will use the premise of a national security review of the U.S. steel industry to demand action by the Group of 20 leaders to reduce excess capacity and other distortions in the global steel market, the top White House economic adviser said on Thursday.

Trump is attending a G20 leaders summit in Hamburg, Germany on July 7-8.

National Economic Council director Gary Cohn told reporters that it was unclear when the Commerce Department will submit its "Section 232" report on the steel industry and potential new import restrictions to the White House.

"It's in the final drafting form. They will be delivering it to the White House at some point," Cohn said. "But the premise of that report we will use as an opportunity to talk with many of our trading partners around the world about what's going on in steel."

U.S. Commerce Secretary Wilbur Ross has said he intended to complete the study by the end of June, but congressional aides and steel industry officials say the timing could slip. The study invokes a Cold War-era trade law that allows the president to restrict imports of goods deemed critical to national defense.

Ross has said he believes there is a "genuine" national security concern over the steel industry's health and one possible remedy is to impose import quotas on certain products coupled with tariffs on any amounts that exceed the quotas.

Ross told a German economic conference that such measures might have to be "broad-scale" but would be aimed at provoking a collective solution to deal with global steel excess capacity.

Cohn told the news briefing on Thursday that Trump would engage in discussions with G20 counterparts about promoting "free and fair trade."

"The United States stands firm against all unfair trading practices, including massive distortions in the global steel market and other non-market practices that harm U.S. workers. We ask the G20 economies to join us in this effort and to take concrete actions to solve these problems."

But Cohn added that the Trump administration "will act to ensure a level playing field for all." (Reporting by David Lawder)