Clinton said she was heartened by Karzai's speech, but also said the reforms and changes pledged had to be implemented.
Along with addressing many US concerns about corruption, however, Karzai also struck a note of defiance after having been heavily criticised by Washington and its allies since the election.
Al Jazeera's James Bays, reporting from the capital, said Karzai raised the detention of Afghan prisoners in American jails and other uncomfortable topics for the US, including the issue of civilian casualties.
"So he was able to make his speech, but it included that central element of corruption that the Americans insisted that they had to hear," Bays said.
Karzai is battling to rebuild his tarnished reputation following a fraud-tainted presidential election on August 20, in which a UN-backed investigation found a third of his votes were fake.
He was named president after Abdullah Abdullah, his main rival, pulled out of a runoff vote complaining that not enough had been done to address the problems of the first round.
Karzai appeared to invite Abdullah and Ashraf Ghani, another election challenger and a former World Bank executive, into a national unity government in Thursday's speech.
"I want to invite both of them to contribute," he said.
Abdullah told the Reuters news agency that he had no plans to accept a role in Karzai's administration.
"It's more of the same," he said.
"He has spoken in these terms, in terms of bringing changes and reform, and fighting corruption, and bringing security and reconciliation, for the last eight years, and the situation has worsened."
Karzai also appeared to call for reconciliation with his Taliban leaders, proposing a "loya jirga", a traditional assembly which under Afghanistan's constitution can take precedence over all government institutions, including the presidency itself.
"We welcome those who are not affiliated with any terrorist organisations and whose hands are not red with Afghans' blood," he said.
But the Taliban also said it would not accept his call for national unity.
"Today is not a historic day. This is a government based on nothing because of the continuing presence of foreign troops in Afghanistan," Zabiullah Mujahid, a Taliban spokesman, told The Associated Press news agency.
Kabul, the Afghan capital, was locked down ahead of the inauguration ceremony.
|Whole neighbourhoods of Kabul were closed off for the inauguration ceremony [AFP]
Regular flights to and from Kabul airport were cancelled for the day and a number of neighbourhoods in the capital were closed to traffic in an attempt to stop attacks.
Karzai addressed the security concerns, saying that Afghanistan's own forces aimed to assume responsibility for security in unstable parts of the country within three years.
Karzai also promised to create thousands of jobs for his impoverished people as part of a reconstruction drive in the country.
Nabi Misddaq, an Afghan scholar and writer, said that the broad nature of the issues covered in Karzai's speech showed the seriousness of the challenges he faces in his next term.
"Challenges from the international community that he must do serious things to bring bribery and all kinds of undesired things that have been going on over the past six years under control," he told Al Jazeera.
"Challenges from Afghans that he has not been a very effective and strong president. And also [the] challenge that the international community is not going to be around [in Afghanistan] for long."