on trade@ (Adds quotes from Trump, context on China)
WASHINGTON, June 30 (Reuters) - U.S. President Donald Trump called for a determined response to North Korea after talks with South Korean President Moon Jae-in on Friday at which he emphasized the importance of their alliance but took aim at Seoul over trade and sharing the cost of defense.
Trump said the United States was renegotiating what he characterized as a "rough" trade deal with South Korea agreed five years ago by his predecessor, Barack Obama, and reiterated that an era of "strategic patience" over North Korea's nuclear and ballistic missile programs had ended.
"Together we are facing the threat of the reckless and brutal regime in North Korea. The nuclear and ballistic missile programs of that regime requires a determined response," Trump said while standing alongside Moon in the White House Rose Garden.
"We're working closely with South Korea and Japan, as well as partners around the world, on a range of diplomatic, security and economic measures to protect our allies and our own citizens from this menace known as North Korea," he said.
Trump called on regional powers to implement sanctions and demand North Korea "choose a better path and do it quickly."
Moon said he and Trump had placed top priority on the North Korean issue and urged Pyongyang to return promptly to talks.
"President Trump and I agreed that only strong security can bring about genuine peace," Moon said. "The threat and provocation of the North will be met with a stern response."
"Our two leaders will employ both sanctions and dialogue in a phased and comprehensive approach" in an effort to resolve the North Korean nuclear issue, Moon added.
Both Trump and Moon have said they are open to renewed dialogue with North Korea, but only under circumstances that will lead to North Korea giving up its weapons programs.
Trump wants China, North Korea's neighbor and main trading partner, to do more to rein in its ally through sanctions.
He sought to woo China after a summit meeting with Chinese President Xi Jinping in April, but has grown frustrated that their relationship has not resulted in stronger action.
STEEL AND AUTOS
While South Korea is a long-standing American ally, Trump has spoken harshly about U.S. trade imbalances and threatened to tear up the bilateral trade pact.
"We will do more to remove barriers to reciprocal trade and market access," Trump said, adding that the two leaders had talked about the thorny trade areas of steel and autos.
"I am encouraged by President Moon's assurances that he will work to create a level playing field so that American workers and businesses, and especially automakers, can have a fair shake at dealing with South Korea," he said.
The U.S. goods trade deficit with South Korea has more than doubled since the KORUS pact 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.
At the start of Friday's talks, U.S. Commerce Secretary Wilbur Ross said the largest component of the deficit was automotive trade and that many non-tariff barriers to U.S. auto exports to South Korea remained.
"There are a lot of various and specific problems, and I think the way to address it is to deal product-by-product with what we can do to change the export side and what we can do to reduce the bad imports side," he said.
Trump stressed the need to ensure equitable sharing of costs for defense, returning to a theme he had raised during his campaign that he has also brought up with other allies, including NATO countries and Japan.
While Trump emphasized the point, a senior U.S. official who held a briefing before the president's meeting with Moon said South Korea was in many respects a "model ally," given its spending of 2.7 percent of GDP on defense and Moon's plan to grow capabilities.
"Burden-sharing is always going to be part of the conversation with our allies. President Trump has made that clear. But we shouldn't view South Korea as somehow laggard on that front," said the official on condition of anonymity. (Reporting by David Brunnstrom, Lisa Lambert, Fatima Bhojani, Roberta Rampton, Tim Ahman and David Lawder; Editing by Yara Bayoumy and Jonathan Oatis)