(Adds discussions on North Korea, paragraphs 8-10)

WASHINGTON/MELBOURNE, March 9 (Reuters) - U.S. President Donald Trump said on Friday he has spoken with Australian Prime Minister Malcolm Turnbull and that they are working on an agreement so Australia will not be subject to U.S. tariffs on steel and aluminum.

"He is committed to having a very fair and reciprocal military and trade relationship," Trump said on Twitter, referring to Turnbull.

"Working very quickly on a security agreement so we don’t have to impose steel or aluminum tariffs on our ally, the great nation of Australia," Trump said.

Australia is a small global exporter of steel despite being one of the world's largest suppliers of the raw commodity iron ore.

Australian steel and aluminum exports to the United States were worth just over A$400 million ($314 million) last year, government data showed.

Shortly after Trump's tweet, Australian Prime Minister Malcolm Turnbull said on Twitter the relationship between the two allies was fair and reciprocal.

"Thank you for confirming new tariffs won't have to be imposed on Australian steel & aluminum - good for jobs in Australia and in US!" Turnbull tweeted.

Turnbull told a news conference in South Australia state his discussions with Trump included the ongoing threats from North Korea after the U.S. president opened the possibility of talks with North Korean leader Kim Jong Un.

"The president and I are both very much of the same mind - that there must be no relenting in the economic pressure on North Korea," Turnbull said.

He said sanctions imposed on North Korea after its missile and nuclear tests must remain until it begins the process of denuclearisation.

($1 = 1.2739 Australian dollars) (Reporting by Eric Beech in WASHINGTON and Alana Schetzer in MELBOURNE Editing by Mohammad Zargham, Leslie Adler and Paul Tait)