Talks are continuing at the UN after divisions emerged at the Security Council over Sunday's rocket test.
China and Russia are both calling for restraint, but Mrs Clinton says the rocket test was a provocative act.
The US military says North Korea failed to show an ability to launch an intercontinental ballistic missile.
US officials say the rocket failed to fire its later stages and fell into the Pacific.
However, analysts say the test was partially successful and should increase North Korea's bargaining power at the negotiating table.
Earlier, the emergency meeting of the Security Council ended without agreement.
"It's a provocative act that has grave implications," Mrs Clinton told reporters.
"North Korea ignored its international obligations, rejected the unequivocal calls for restraint, and further isolated itself from the community of nations."
She added: "We know that working out the language is not easily done overnight but we remain convinced that coming out with a strong position in the United Nations is the first and important step that we intend to take."
As divisions emerged, diplomats said the Security Council would continue talks but correspondents say it may take days for a deal.
Washington and Tokyo are seeking a strong response, but Beijing and Moscow have called for restraint.
Pyongyang says it launched a satellite early on Sunday but its neighbours say it was testing missile technology.
The US, South Korea and Japan have all condemned the launch from the Musudan-ri base in the north-east of the communist country.
They say it violates a UN Security Council resolution adopted in October 2006 which bans North Korea from carrying out ballistic missile activity.
Susan Rice, the US envoy to the UN, called Pyongyang's move a "clear-cut violation of [resolution] 17-18", while her Japanese counterpart said Tokyo was seeking a "clear, firm and unified" response.
But, says the BBC's Laura Trevelyan, who is at the UN in New York, countries such as China and Russia disagree.
There was no general agreement at the council on whether North Korea was in breach of the resolution, let alone on whether it should be punished, our correspondent says.
The Japanese government, meanwhile, said it would be considering possible new bilateral sanctions against North Korea over the course of the next few days.
HAVE YOUR SAY
For those of you who claim that North Korea has the right to test rockets... OK... but how you feel about one coming over your country without permission being given... get real!
Richard, Kobe, Japan
North Korean state media said that leader Kim Jong-il had visited the General Satellite Control and Command Centre to observe the launch.
It said a communications satellite had been successfully placed in orbit and was transmitting data.
But the US military said that the rocket's payload, along with its booster stages, landed in the Pacific Ocean.
Pyongyang's neighbours are concerned about the potential military use of the launch vehicle, and believe North Korea's real aim was to test the long-range Taepodong-2 missile.
