The strategy was announced after a special briefing for all 100 US senators.
Earlier, the top US commander in the Pacific defended the deployment of an advanced missile defense system in South Korea.
Tensions in the Korean Peninsula raised amid fears North Korea is planning new weapons tests.
A joint statement issued by Secretary of State Rex Tillerson, Defense Secretary Jim Mattis and Director of National Intelligence Dan Coats said: “The United States seeks stability and the peaceful denuclearisation of the Korean peninsula.
“We remain open to negotiations towards that goal. However, we remain prepared to defend ourselves and our allies.
“The president’s approach aims to pressure North Korea into dismantling its nuclear, ballistic missile, and proliferation programs by tightening economic sanctions and pursuing diplomatic measures with our allies and regional partners.”
The US already has extensive sanctions in place on North Korea, including a blanket ban on trade and a blacklist of anyone dealing with North Korea.
It is not clear what further sanctions the US could impose.
Democratic Senator Christopher Coons told reporters that military options were discussed at the special presidential briefing for senators.
“It was a sobering briefing in which it was clear just how much thought and planning was going into preparing military options if called for – and a diplomatic strategy that strikes me as clear-eyed and well-proportioned to the threat,” he said.
A White House official said an option under consideration was to put North Korea back on the state department’s list of countries that sponsor terrorism.
President Trump’s predecessor, Barack Obama, imposed sanctions over a year ago following a nuclear test and satellite launch by North Korea.
North Korean government property in America was frozen and US exports to, or investment in, North Korea was banned.
The order also greatly expanded powers to blacklist anyone, including non-Americans, dealing with North Korea.
The senators received a highly unusual briefing by the Trump administration on the seriousness of the threat from North Korea and Donald Trump’s strategy for dealing with it on April 26.
Earlier Admiral Harry Harris, head of US Pacific Command, said the US would be ready “with the best technology” to defeat any missile threat.
The deployment of Terminal High-Altitude Area Defense (THAAD) system in South Korea was aimed, he argued, at bringing North Korean leader Kim Jong-un “to his senses, not to his knees”.
Admiral Harry Harris said he believed that North Korea would try to attack the US as soon as it had the military capabilities.
China says the deployment of THAAD will destabilize security and there have been protests in South Korea itself, where three people were injured in clashes with police as the system was being delivered to a former golf course on April 26.
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