A majority of Americans said they would support a military response to a North Korean launch of a long-range ballistic missile, a poll shows, even as the Obama administration has sought a diplomatic response from within the United Nations.

Forming a consensus that reaches across the political spectrum, 57 percent of Americans support using the military to eliminate North Korea's missile-launching capability, according to a poll from Rasmussen Reports.

In a survey conducted during the two days before Saturday's launch, 66 percent of Republicans and 52 percent of Democrats said they supported the military option if North Korea went ahead with the missile test. The telephone survey of 1,000 likely voters had a margin of error of 3 points.

The U.S. and South Korean governments have steadfastly opposed a military response to the North Korean action, which both Seoul and Washington called a "provocative act." No regional powers made an attempt to shoot down the three-stage Taepodong-2 rocket, which has a potential range of 5,000 miles and flew over the Japanese mainland early Sunday local time.

The Obama administration considers Pyongyang in violation of U.N. Security Council Resolution 1718, which prohibits North Korea from conducting ballistic missile-related activities and tests. The White House is seeking action at the Security Council in response to the launch, which Pyongyang claims was intended to shoot a communications satellite into space.

That puts the president and his cabinet in the 15 percent of Americans who oppose a military response. Twenty-eight percent of those polled said they were not sure.

U.S. intelligence officials reportedly say the rocket traveled nearly 2,000 miles from its launch site in North Korea -- more than half the distance to Anchorage, Alaska.

Click here to see the poll from Rasmussen Reports.