(Adds Feinstein comments in paragraphs 13-16)
WASHINGTON, Aug 31 (Reuters) - Senator Robert Menendez, Chairman of the Senate Foreign Relations Committee, called on Sunday for the United States to arm Ukraine in its effort to repel what he called a Russian invasion.
"We ... should be providing the Ukrainians with the types of defensive weapons that will impose a cost upon (Russian President Vladimir) Putin for further aggression," the New Jersey Democrat told CNN's "State of the Union" program from Kiev.
He said the European Union, NATO and the United States should work together to arm Kiev, which has been fighting Russian-backed rebels in eastern Ukraine for several month.
Asked whether the Obama administration is considering such a move, Menendez said: "I think that may very well be on the table right now. These are changed circumstances."
President Barack Obama last week again ruled out U.S. military action over Ukraine and said there must be a diplomatic solution.
The Obama administration has stopped short of calling Moscow's intensified support for separatist forces in eastern Ukraine an invasion, and has said sanctions are the most effective tool in dealing with Russia's actions in Ukraine.
Representative Mike Rogers, chairman of the House Intelligence Committee, said it was imperative for the United States and Europe to provide strategic help to Ukraine now to halt what he called Russia's increasingly aggressive actions.
"If we don't provide 'small and effective' now, you're going to get very big and very ugly later," Rogers, a Michigan Republican, said on "Fox News Sunday." "Now is the opportunity to make that decision and ... not make the same mistake the president made in Syria."
Menendez called for stepping up sanctions on Russia, saying that the United States should impose sectoral sanctions on Russian companies in the financial and energy industries.
Putin called on Sunday for immediate talks on "statehood" for southern and eastern Ukraine, although his spokesman said this did not mean Moscow now endorsed rebel calls for independence for territory they have seized.
Kiev and its allies in Europe and the United States, who have imposed sanctions against Russia over its role in Ukraine, say a new separatist offensive in its east has been backed by armored columns of more than 1,000 Russian troops.
"This is a direct invasion by Russia. It's not rebels, it's Russian soldiers," Menendez said.
FEINSTEIN QUESTIONS SANCTIONS' EFFECTIVENESS
Senator Diane Feinstein, chair of the Senate Intelligence Committee, said sanctions may fail to sway Moscow because the restrictions would be slow to affect the Russian people, who are standing behind Putin.
"I'm not sure they will work. I'm not sure that it shakes the people that much. And it's the people that have to be spoken to," she said on NBC's "Meet the Press" program.
Feinstein, a Democrat from California, said Washington needs to engage directly with Putin.
"I think there ought to be steps taken to send people to talk with him, to have our secretary of state talk with him personally," she said. (Reporting by Michael Flaherty and Andrea Shalal; Editing by Mohammad Zargham)