North Korea conducted a fourth nuclear test in January and a long-range rocket launch the next month, both in contravention of U.N. Security Council resolutions.
Expanded U.N. sanctions aimed at starving North Korea of funds for its nuclear weapons programme were approved in a unanimous Security Council vote in early March on a resolution drafted by the United States and China.
Blinken, who is meeting senior Japanese government officials in Tokyo, told reporters North Korea would be digging itself deeper into a hole if it pursued further provocations.
"There will be additional strong response in case of another (North Korean) nuclear test," Blinken said, adding that such actions by North Korea were "unacceptable".
Blinken said the United States would consider "a number of possibilities" while adding that it was "premature" to be specific.
Some experts expect North Korea to conduct its fifth nuclear test in the near future, possibly before its party congress in early May, following the embarrassing missile failure on Friday.