The trip comes at a time of heightened tensions between the USA and North Korea, which has conducted missile tests and detained four American citizens.
Tillerson told USA senators at the start of a budget hearing that the State Department had no comment on Mr Warmbier's condition, "out of respect for him and his family". In March, 2016 Warmbier was sentenced to 15 years of hard labor in the country for stealing a propaganda poster.
Warmbier had been arrested while visiting North Korea with Young Pioneer Tours. "But we have issued travel warnings to Americans and suggested they not travel to North Korea for their own safety", he said.
Since last March, the USA had been pressing North Korea to let Swedish officials see the four Americans, a senior State Department official told CNN.
His entourage includes Joseph Terwilliger, a professor who has accompanied Rodman on previous trips to North Korea.
Rodman, in an interview with CNN before landing in North Korea, said he was "trying to accomplish something we both need", referring to himself and the Trump administration. It wasn't immediately clear whether his release was connected to Rodman's visit.
Yun then met last week with the North Korean ambassador at the U.N.in NY. Tillerson did not discuss Warmbier's medical condition. A person who answered the phone at Warmbier's family's OH residence said: "No comment, thank you" and hung up.
State Department spokeswoman Heather Nauert, asked whether Warmbier's release could open the way for dialogue amid high tensions between the Trump administration and North Korea, said "it's just too soon to say". "We get to see our son Otto tonight".
Britain voted against May's majority in Parliament - but what about Brexit?
The EU negotiators will know that they are negotiating with someone who may not be able to give the final word. Mrs Merkel added she hoped Britain would remain a good partner following the talks, due to begin on 19 June .
Although he confirmed that Warmbier has been released, Tillerson could not comment on Warmbier's health.
The White House says a US envoy met with North Korean foreign ministry representatives in Norway last month as part of efforts to win freedom for Americans held by Pyongyang.
Before his trial, Mr Warmbier said he tried to steal the propaganda sign as a trophy for an acquaintance who wanted to hang it in her church.
Americans have been sentenced to years in North Korean prisons for seemingly minor offenses and likely could not expect leniency if the country's drug laws were violated.
He was last seen during his hour-long trial last March for "hostile acts against the state", and hasn't been in the public eye since.
A statement issued in NY by a Rodman publicist said the former National Basketball Association player is in the rare position of being friends with the leaders of both North Korea and the United States.
"North Korea should be universally condemned for its abhorrent behavior".
Speaking to reporters in Beijing before his arrival in Pyongyang on Tuesday, he said that the issue of several Americans detained by North Korea is "not my goal right now".
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