Liu was jailed in 2009 for 11 years for "inciting subversion of state power" after he helped write a petition known as "Charter 08" calling for sweeping political reforms in China.
In a scathing attack on the Chinese government the Norwegian Nobel Committee, which awards the prize, said the Chinese government bore "heavy responsibility" for the death of the Nobel Peace Prize laureate.
Now, the United States and the European Union have urged the Chinese government led by President Xi Jinping to let Liu's widow, Liu Xia, who has been under house arrest since 2010 to leave the country.
"I call on the Chinese government to release Liu Xia from house arrest and allow her to depart China, according to her wishes," US Secretary of State Rex Tillerson said.
The EU urged Beijing to let Liu Xia and his family bury him "at a place and in a manner of their choosing, and to allow them to grieve in peace".
Jared Genser, a US lawyer who represented Liu, said all contact with Liu Xia had been cut off in the past 48 hours.
China has however rejected foreign criticism saying it was a "domestic matter" and "all-out" efforts had been made to treat him.
"China is a country under the rule of law. The handling of Liu Xiaobo's case belongs to China's internal affairs, and foreign countries are in no position to make improper remarks," foreign ministry spokesman Geng Shuang was quoted as saying by the official Xinhua news agency.
US and EU have urged the Chinese government to let Liu's widow, Liu Xia, who has been under house arrest since 2010 to leave the country. ||||Liu Xiaobo was diagnosed with late stage liver cancer, even though several countries were ready to treat him in their own country.