WASHINGTON, March 13 (Reuters) - Russia is showing signs of a willingness to engage in substantive negotiations over Ukraine, even as Moscow currently is intent on "destroying" its neighbor, U.S. Deputy Secretary of State Wendy Sherman said on Sunday,

Sherman, in an interview with "Fox News Sunday", said the United States is putting "enormous pressure" on Russian President Vladimir Putin to agree to a cease-fire in its weeks-old invasion of Ukraine and to allow the creation of humanitarian corridors to allow civilians to escape.

"That pressure is beginning to have some effect. We are seeing some signs to have real, serious negotiations. But I have to say ... so far it appears Vladimir Putin is intent on destroying Ukraine," Sherman said.

Following a Russian attack on a military base near Poland's border where NATO defenses are deployed, Pentagon spokesperson John Kirby said he did not believe a NATO-imposed no-fly zone over Ukraine would have prevented that.

And he said that while a no-fly zone has a "nice air policing sound," such a move by NATO would hurl the United States into war with Russia.

"There is very little that you can see that would make sense for this war to be escalated between two nuclear powers," Kirby told ABC's "This Week."

(Reporting by Richard Cowan and Sarah N. Lynch; Editing by Lisa Shumaker)