The calls for a response come as spy satellites detected new activity at North Korea's underground nuclear test site for the first time in several weeks, according to two United States officials who spoke to CNN.
Trump, addressing Warmbier's detention during brief remarks in the Oval Office, said, "It should never, ever be allowed to happen".
Officials from Trump down have expressed sadness about the college student's fate, but say that for now, they haven't decided on a course of action.
The Chinese "have limited capacity to do something, and I think they feel the weight of expectations beginning to burden them", said Christopher Hill, who led the USA delegation in the six-party talks with North Korea during the George W. Bush administration. "We're still considering our options".
Obama's office had no reaction, but his former aides have said he worked tirelessly to try to get Warmbier and other Americans released from North Korea.
But North Korea has also consistently lobbied Washington for specific concessions that would need deep negotiations, something recent USA administrations have been reluctant to pursue because of the North's weapons programs.
The usual menu of retaliatory measures against North Korea include sanctions that target its businesses and officials.
Schiff said a new law was important to show Congress' unity on North Korea, arguing that financial measures through the Treasury Department might be more effective than a passport ban because it would deter travel companies ferrying Americans.
Sen. Bob Corker of Tennessee, the Republican chairman of the Foreign Relations Committee, said the USA should think about banning US citizens from visiting North Korea.
Amit Shah declines to comment on Presidential candidates
The BSP leader further added that she would wait and watch if Opposition announces a Dalit candidate as well. He added that farmers have not committed any crime but actually brought a revolution.
"We can launch and operate long-range bombers over the Korean peninsula on very short notice, and we hope not to have to do that", Pentagon spokesman US Navy Capt. Jeff Davis said.
The US regularly conducts "assurance and deterrence" bomber flights with its military partners in the region, but the drills are often criticized by North Korea as provocative acts. Maria Cantwell, called for licensing of humanitarian groups that enter the country.
Some observers believe that North Korea became anxious because Warmbier's condition suddenly worsened. The bill would require the Treasury to issue regulations requiring a license for transactions related to travel to, from and within North Korea by USA citizens - and bar licenses for tourist travel.
Trump condemned Pyongyang following news of his death. John McCain, Minnesota Democratic Sen.
The North Korean government handed Warmbier over to U.S. authorities in a vegetative state last week and his death has spurred calls for a USA response from several lawmakers.
The Trump statement about China was likely to increase pressure on Beijing ahead of Wednesday's Diplomatic and Security Dialogue, which will pair U.S. Secretary of State Rex Tillerson and Defense Secretary James Mattis with China's top diplomat, State Councilor Yang Jiechi, and General Fang Fenghui, chief of state of the People's Liberation Army.
Nauert stressed that the State Department issued a travel warning for North Korea that lays out the dangers.
"We don't have a lot of leverage, but I would support the travel ban", he told reporters Tuesday.
Still, Americans continue to travel there for the novelty as well as to teach in universities and do discreet missionary work. He was put before North Korean officials and journalists for a televised "confession". He was sentenced to 15 years of hard labour for trying to steal an item bearing a propaganda slogan from his hotel in Pyongyang, the nation's state media said.
Warmbier, 22, died Monday in OH, just five days after being returned from North Korea.
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