UPDATE 2-Trump says determined response needed on North Korea, takes aim at Seoul on trade

Seoul on trade@ (Recasts with news conference)

WASHINGTON, June 30 (Reuters) - U.S. President Donald Trump emphasized the need for a determined response to North Korea after talks with South Korean President Moon Jae-in, while taking aim at Seoul over trade and the need for burden sharing in defense.

At a joint appearance with Moon, Trump said North Korea's nuclear and ballistic missile programs required a "determined response," and reiterated that an era of "strategic patience" with the North Korean government had ended.

"The era of strategic patience with the North Korean regime has failed. ... Frankly, that patience is over," 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."

Trump said at the start of his second day of talks with Moon that the United States was renegotiating what had been a "rough" trade deal with South Korea.

"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.

Trump also stressed the need to ensure equitable sharing of costs for defense between the United States and South Korea. (Reporting by David Brunnstrom; Editing by Yara Bayoumy and Jonathan Oatis)