The 47-member forum met at the request of Britain and the European Union to consider a resolution calling for the release of ousted Myanmar leader Aung San Suu Kyi, and for United Nations monitors to be allowed to visit.
"What happened in Myanmar is essentially Myanmar's internal affairs", said Chen Xu, China's ambassador.
The sponsors of council resolutions often agree to soften the language of their texts in order to win consensus and to show that the 47-member body is united on thorny human rights issues.
On Wednesday, President Joe Biden said the United States will sanction Myanmar military leaders - with a first round of targets to be identified soon - and impose strong export controls to force the military to reverse course.
"We regret that our office has always been denied a presence in Myanmar, and urge the military authorities to grant the Office of the High Commissioner for Human Rights (OHCHR) and the special rapporteur on the human rights situation in Myanmar full and immediate access", she added.
The council has no power to impose sanctions but can train a political spotlight on rights abuses and violations.
The deputy high commissioner said: "The world is watching".
The council urgently called for the release of Daw Suu, President U Win Myint and over 220 others arbitrarily detained, as well as the lifting of the state of emergency, which has been in place since February 1.
Thomas Andrews, the UN rights investigator for Myanmar, told a special session of the rights council in Geneva that the UN Security Council should consider imposing sanctions and arms embargoes.
"The message from the people of Myanmar to all of you and to the people of the world is clear: This can not stand", he said.
Arbitrary detentions and intimidation were also on the rise, with at least 220 government officials and members of civil society arbitrarily detained.
The military staged a takeover last week, claiming that the general election late previous year that brought a landslide victory to Daw Aung San Suu Kyi's then-ruling National League for Democracy was stolen, contrary to the assertions of local and global election observers.
Anger in Myanmar has been fuelled by videos showing more arrests of government critics, including a doctor who was part of the civil disobedience movement.
In the nation's business hub, Yangon, people called others outside to gather and protest by banging pots and pans - an action traditionally associated with driving out evil in the country.
The aide, Mr Kyaw Tint Swe, had served as minister for the office of the state counsellor under Ms Suu Kyi, who has been detained since the Feb 1 coup.
"These designations specifically target current or former members of the military who played a leading role in the overthrow of Burma's democratically elected government".
Wearing a mask in a almost empty hall at the UN Geneva amid the coronavirus pandemic, Myanmar's ambassador, Myint Thu, largely gave general commitments from his country, such as helping internally displaced people or fighting Covid-19. The election commission has said there is no evidence to support those claims.
He took office in October under Suu Kyi's government, but justified the military's actions.
Myanmar, speaking as a concerned country at the council, reiterated that in light of the post-election irregularities, the Tatmadaw was compelled to take "State responsibilities in accordance with the State Constitution".
Other experts have also warned against hastily deciding on sanctions against Myanmar, a country that had been promoting democratic reforms since the first civilian government was voted in in 2015. "Myanmar's democratic transition depends on it".
"We will also continue our support for the Rohingya and other vulnerable populations", Psaki said.
Russian ambassador Gennady Gatilov said: "Attempts to whip up hype around the situation in Myanmar need to cease".
About the Rohingyas, Nada al-Nashif said: "The military authorities must not be allowed to exacerbate the situation of the Rohingya people, after the extreme violence and decades of discrimination that they have endured".