"On behalf of President Obama and the people of the United States, I congratulate the people of China as you celebrate your National Day this October 1," Clinton said in her message, the State Department reported on its Web site Friday.
This year's National Day marks the 62nd anniversary of the founding of the People's Republic of China in 1949.
The message said the United States has shown a deep commitment to the U.S.-China relationship as envisioned by their leaders.
"The United States is committed to the success of China because a thriving China is good for America and a thriving America is good for China," the message said. "Our two peoples are known for their hard work and ingenuity and it is clear that by working together we can find solutions to our most pressing global challenges."
China's official Xinhua news agency, reporting Clinton's message, said it came one week after Washington announced "a $5.85 billion package of arms sales to the Chinese island of Taiwan despite Beijing's strong opposition."
China has been criticizing the United States for the deal, which will be used to upgrade of Taiwan's F-16 A/B fighters, calling it a "serious blow" to U.S.-China relations.
In a recent statement, the Chinese foreign minister asked the United States to "correct its error" by immediately revoking the deal.
China claims Taiwan as part of its territory although the two have had separate governments since 1949.