(Adds quotes from Moon speech at business forum)

By Jeff Mason and David Brunnstrom

WASHINGTON, June 28 (Reuters) - U.S. President Donald Trump will press South Korean President Moon Jae-in to improve trade imbalances with the United States during meetings at the White House on Thursday and Friday, a White House official said.

Moon, whose talks with Trump will focus largely on efforts to press North Korea to give up its nuclear weapons program, did not directly address Trump's concerns in a speech at the U.S. Chamber of Commerce on Wednesday evening, emphasizing instead an increase in the total volume of bilateral trade.

In an interview with Reuters in April, Trump called the five-year-old U.S.-South Korean trade pact known as KORUS "horrible" and "unacceptable" and said he would either renegotiate or terminate it.

A White House official told reporters that Trump would raise concerns about barriers to U.S. auto sales and "the enormous amount of steel that sometimes ends up being surplus Chinese steel that comes to the United States via South Korea."

The official, however, predicted "a friendly and frank discussion about the trade relationship."

At the Chamber of Commerce, Moon said that under his economic policy, unfair trade practices would be eradicated and factors that limited competition, such as market entry barriers and price regulations, would be "reevaluated."

He said that in spite of a 12 percent decrease in global trade over the last five years, bilateral trade had risen by this amount.

"The U.S. market share in Korea's import market has increased and Korea has also seen an increase in its share of the U.S. important market," he said. "Expansion of bilateral trade is enriching the daily lives of our peoples."

Moon, on his first overseas trip since taking office on May 10, said he hoped his visit would provide an opportunity to reaffirm the U.S. alliance and elevate economic ties "to the next level."

"Both our countries have new governments in place; let us become best partners by creating new jobs in our countries," Moon said. "Let us move forward hand in hand towards a path of joint and common prosperity."

The U.S. goods trade deficit with South Korea has more than doubled since KORUS took effect in 2012, from $13.2 billion in 2011 to $27.7 billion in 2016. It was forecast to boost U.S. exports by $10 billion a year, but they were $3 billion lower in 2016 than in 2011.

The Trump administration is considering whether to impose tariffs or quotas on steel imports.

In April, Trump ordered an investigation under the rarely used section 232 of the Trade Expansion Act of 1962 that allows restrictions on imports for reasons of national security.