The removal of more than 111 pounds of highly enriched uranium followed a pledge by Ukrainian President Viktor Yanukovych to get rid of all of his country's highly enriched uranium by April 2012.
"Ukraine, they recognize they're part of the international community, they recognize how dangerous this material is," Thomas D’Agostino, head of the National Nuclear Security Administration, told Maddow.
The material will be blended down in Russia, rendering it useless for bomb making, the Associated Press said.
Yanukovych agreed to give up the uranium in a multinational deal announced at a nuclear security summit hosted by President Barack Obama in April. Shipments like the one recently completed from Serbia result in permanent threat reduction because they eliminate weapons-usable nuclear material at civilian sites.
Securing the material will prevent it from falling into the wrong hands, officials say.
As an incentive, the United States is providing replacement low-enriched uranium that can be used for Ukraine's research reactors.
The summit deal also has the United States building a $25 million "neutron source facility" nuclear research project for Ukraine, the administration said. The facility will be able to produce 50 different types of medical isotopes, using only low-enriched uranium.
"The fewer places this stuff is at the better off the world is," D'Agostino told Maddow. "This is a global problem."
"It doesn't require a lot of technology or knowhow to make a nuclear bomb," he said. "Unfortunately the word is out there."
The "vulnerable nuclear material" was in 35 nations, D'Agostino said.
"We're done with 19 countries and have 16 more to go," D'Agostino told Maddow, noting the U.S. and other countries were on track to complete removal by the end of the four-year deadline established by the nations.
All the movement has to be done in secret and coordinated with other nations, he said.
Four nations were involved in the Ukraine operation, he said.
"Pulling this off is a huge challenge," he said.
The removal operation completed Thursday involved 21 specially designed casks for the uranium to be flown on five flights from three cities, officials told The Associated Press.
The operation was delayed for days by ice storms in Ukraine. The U.S. also helped deliver some of the replacement fuel to Ukraine.
"This may have been the most complicated operation NNSA has done in recent years," said Andrew Bieniawski, the U.S. agency's associate deputy administrator for global threat reduction.
The uranium came from three research facilities, in Kiev, Sevastopol and Kharkiv. The U.S. also helped Ukraine remove a slightly larger amount of spent uranium by rail in May. An additional amount of uranium remains in Ukraine, but the U.S. said the material was on track to be removed by the April 2012 deadline.
On Dec. 22, 28 pounds of Russian-origin highly enriched uranium spent fuel was removed from the Vinca Institute of Nuclear Sciences in Serbia, making that nation the sixth country to eliminate all of its stockpiles of the material since April 2009, the nuclear security agency said after an operation there.
The agency has removed or assisted with the disposition of enough material to make more than 122 nuclear weapons, it said.
About 3.5 million pounds of highly enriched uranium and half a million pounds of bomb-grade plutonium remain in the world, according to Harvard University's Belfer Center.
That material could be used to build as many as 200,000 nuclear weapons, or about 8 1/2 times the world's current stockpile of 23,360 warheads.