China had given a nervous welcome to US President Barack Obama, fearing the Democratic leader will press the world's most populous nation harder on human rights and trade issues than his predecessor George W Bush.
Clinton appeared to be trying to assuage those concerns as she left Seoul for Beijing, where she was holding talks on Saturday.
She said that while the United States would continue to raise longstanding rights concerns with China, "our pressing on those issues can't interfere on the global economic crisis, the global climate change crisis and the security crisis."
T Kumar of Amnesty International USA said the global rights lobby was "shocked and extremely disappointed" by Clinton's remarks.
"The United States is one of the only countries that can meaningfully stand up to China on human rights issues," he said.
"But by commenting that human rights will not interfere with other priorities, Secretary Clinton damages future US initiatives to protect those rights in China," he said.
Sophie Richards, Asia advocacy director for Human Rights Watch, said pressure was needed to consolidate progress made in China in rights including labor protections and relaxing restrictions against foreign journalists.
"A successful strategy for the US doesn't entail 'agreeing to disagree,' but rather convincing China it is in its own interest to protect dissent, peaceful protests and the creation of a truly independent legal system," Richards said.
Clinton's visit comes weeks before the sensitive 50th anniversary of a 1959 uprising against China's rule in Tibet that culminated in the Himalayan territory's spiritual leader the Dalai Lama fleeing into exile in India.
Tenzin Dorjee, deputy director of the New York-based advocacy group Students for a Free Tibet, said that Clinton was sending the wrong signal at a time that China is pouring troops into Tibet.
"The US government cannot afford to let Beijing set the agenda," Dorjee said.
"Leaders really need to step up and pressure China. It's often easy to wonder whether pressure makes a difference. It may not make a difference in one day or one month, but it would be visible after some years," Dorjee said.
Dorjee said that Tibetans had been heartened by Obama's inauguration speech, in which he said that regimes that quash opposing ideas were "on the wrong side of history." Chinese state television censored translations of the speech.
Amnesty International and Human Rights Watch had sent a letter to Clinton before her maiden Asia visit urging her to raise human rights concerns with Chinese leaders.
Before she left, State Department spokesman Robert Wood said human rights would be "an important issue" for Clinton and that she would "raise the issue when appropriate."
Also voicing dismay over Clinton's remarks in Asia was the US Campaign for Burma, which is pressing for democracy and human rights in military-run Myanmar.
Jeremy Woodrum, the group's co-founder, urged Clinton to retract her statement and said she had a strong human rights record as a senator.
"Stating that human rights are not a major priority is a mistake and detrimental to all those suffering human rights abuses who were depending upon the new US administration," he said.