His tweet comes a day after learning that Otto Warmbier, an American student who was returned from North Korea to the U.S.in a coma last week, had died.
"We have a great deal of resolve to try to handle the situation and try to hold North Korea responsible for the death of Mr. Warmbier and bring back those three Americans who do remain there", Nauert added.
White House spokesman Sean Spicer said a meeting between Trump and North Korean leader Kim Jong Un is less likely following Warmbier's death.
Warmbier arrived in North Korea on an organized trip in January last year and was arrested for trying to steal a propaganda poster from a Pyongyang hotel and sentenced to 15 years of hard labor.
Warmbier died at the University of Cincinnati Medical Center after returning home with a "severe neurological injury" that left him in a state of "unresponsive wakefulness", doctors said last week.
"Otto Warmbier should never have been in jail for tearing down a stupid banner".
The US sent B1-B bombers - which are capable of carrying nuclear weapons - to the border of North Korea hours after his death. Delury, of Yonsei University, said that Beijing could apply more pressure by suspending tour groups from North Korea until USA prisoners are released.
The usual menu of retaliatory measures against North Korea include sanctions that target its businesses and officials.
"It's a total disgrace what happened to Otto", Trump said during an event in the Oval Office.
Richardson praised President Donald Trump for his administration's push to win Warmbier's release.
Warmbier died Monday in his home state of OH, his family said, six days after being freed in a coma by North Korea. The doctors in Cincinnati said they found no sign of botulism and that the cause of his brain injury was unclear.
Russian fighter comes within feet of Air Force recon plane
The Russians claim that they intercepted the reconnaissance aircraft as the plane "approached the Russian state border". The tensions are mounting today between the US and Russian Federation , which sides with the Syrian regime.
Corker also said Warmbier's death "just stirs up this anger towards North Korea".
South Korea's Blue House on Tuesday cited President Moon separately as saying: "It is very deplorable that North Korea does not respect human rights". Pyongyang has also vowed to develop a nuclear-tipped intercontinental ballistic missile capable of hitting the US mainland.
A team of USA doctors have also disputed North Korea's version of events.
"It really is a tragedy. I think there have been some positive steps they have taken both at the United Nations and economically to help strengthen the case against North Korea", Spicer said. China has backed the Kim dynasty since the Korean War, in part to keep US troops away from its border.
Mr Trump made the announcement as he also appeared to blame his predecessor Barack Obama over the death of Otto Warmbier, 22, the United States student who died after being imprisoned for 17 months in North Korea.
Mr Warmbier was on a tourist trip when he was arrested and handed a 15-year sentence in March last year, a punishment U.S. officials decried as out of proportion to his alleged crime.
"I thought American citizens might be treated better than South Koreans but looking at Otto's case it is shocking". John McCain, R-Ariz., proposed that prospective American travelers complete a form declaring they won't hold the US government responsible for what happens.
Warmbier died in OH on Monday, days after being released by North Korea. And I spoke with his family. "We obviously want humanitarian work to continue in North Korea, but I think we need to think hard about making it safer for our citizens who do travel there".
The U.S. often uses the bombers to show strength in response to hostile actions carried out by North Korea's Stalinist regime, such as ballistic missile tests or nuclear tests.
Uri Tours, which is based in the U.S. and has an office in Shanghai, said it was "reviewing" its position. DPRK is short for the Democratic People's Republic of Korea, North Korea's official title.
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