Not all Americans want a missile defence shield
The test was originally scheduled for Saturday, but poor atmospheric conditions could have made it unsafe, the Pentagon said.
President George W Bush wants to build a shield to protect the United States against ballistic missiles fired from rogue countries but the plan is strongly opposed by Russia, China and many other states.
The test - consisting of launching a dummy warhead on a prototype Minuteman 2 booster rocket and then shooting it down with an interceptor missile - is now expected to be carried out on Monday night local time.
The dummy is to be fired from Vandenberg Air Force Base in California, while the interceptor will be launched from Kwajalein Atoll in the Marshall Islands.
Two previous attempts by the US military to down dummy warheads have failed, and two have succeeded.
Russian, Chinese objections
The interceptor missile is to be launched about 20 minutes after the dummy missile is fired.
The US missile defence programme has put Washington on a collision course with Russia and China. Both countries have said it will start a new arms race.
The 1972 Anti-Ballistic Missile Treaty between the United States and the former Soviet Union barred both countries from building a national missile defence shield.
The test to be carried out would not violate the treaty, according to US officials.
President Bush and Russian President Vladimir Putin failed to agree on scrapping or changing the treaty at a recent summit - although they did agree to cut offensive nuclear missiles.