Washington - President Barack Obama will use his State of the Union speech on Tuesday to reinvigorate one of his signature national security objectives - drastically reducing nuclear arsenals around the world - after securing agreement in recent months with the United States military that the U.S. nuclear force can be cut in size by roughly a third.

Obama, administration officials say, is unlikely to discuss specific numbers in the address, but White House officials are looking at a cut that would take the arsenal of deployed weapons to just above 1,000. Currently there are about 1,700, and the new strategic arms reduction treaty with Russia that passed the Senate at the end of 2009 calls for a limit of roughly 1,550 by 2018.

But Obama, according to an official who was involved in the deliberations, "believes that we can make pretty radical reductions - and save a lot of money - without compromising American security in the second term. And the Joint Chiefs have signed off on that concept."

The big question is how to accomplish a reduction that Obama views as long overdue, considering that Republicans in the Senate opposed even the modest cuts in the new arms reduction treaty, called New START. The White House is loath to negotiate an entirely new treaty with Russia, which would lead to Russian demands for restrictions on U.S. and NATO missile-defense systems in Europe and would reprise a major fight with Republicans in the Senate over ratification.

Instead, Obama is weighing whether to announce unilateral cuts or, more likely, to attempt to reach an informal agreement with President Vladimir V. Putin of Russia for mutual cuts within the framework of the New START - but without the need for ratification. Obama's national security adviser, Tom Donilon, is planning to travel to Russia next month, officials say, to lay the groundwork for those talks.

Within days of the State of the Union address, officials say, he plans to issue a long-anticipated presidential directive on combating cyberattacks aimed at U.S. companies, financial institutions and critical infrastructure like the electric grid.

The announcement comes at a moment of heightened attacks from China and, most recently, from Iran.