American lawmakers defied President Barack Obama and approved fresh economic sanctions against Russia, prompting swift criticism from Moscow Friday over toughening the US response to a Kremlin-backed separatist insurgency in Ukraine.

The legislation also authorizes -- but does not legally require -- Obama to provide lethal and non-lethal military aid to Ukraine, including anti-tank weapons, ammunition and "tactical troop-operated surveillance drones."

The sanctions bill was passed unanimously Thursday in the Senate and House of Representatives. Because of a technical issue it returns to the Senate, where aides say there likely will be unanimous consent for final passage as early as Friday.

Asked whether the president would sign it, White House spokesman Josh Earnest said "we are looking at it right now."

Washington backs Ukraine in its conflict with Russia, but Obama has yet to approve the bulk of an arms request by Kiev.

The bill's coauthor Senator Bob Corker criticized the delay as a "hesitant US response to Russia's continued invasion of Ukraine."

Final passage of the sanctions would heap political pressure on the president.

But on Thursday Obama signalled he was against unilaterally putting the economic squeeze on Moscow, saying it would be "counterproductive" for Washington to "get out ahead of Europe further" on sanctions.

"The notion that we can simply ratchet up sanctions further and further and further, and then ultimately Putin changes his mind, I think is a miscalculation," Obama said.

Washington coordinated with the European Union to impose tough sanctions on Russia in September. While they have bitten into the Russian economy, Putin dismissed the punitive measures and said the West was using Ukraine as an international pawn.

In November, the Pentagon delivered the first of 20 anti-mortar radar systems to Ukraine.

The current legislation authorizes $350 million worth of weapons, defense equipment and training for Ukraine over three years.

Lawmakers dropped a key provision in the original bill that would have taken the rare step of designating Ukraine, Georgia and Moldova as major non-NATO allies of the United States.

Senate aides said the provision was removed at the 11th hour in order to ensure final passage.

The measure hits Russia's defense and energy sectors, punishing companies like state defense import-export company Rosoboronexport.

It requires Obama to impose conditional sanctions on the defense sector should Russian state-controlled firms sell or transfer military equipment to Syria, or to entities in Ukraine, Georgia or Moldova without the consent of the governments in those nations.

The rule is aimed at helping stem the flow of weapons from Russia across the border into eastern Ukraine, where Washington and Kiev accuse Moscow of fomenting separatist unrest.

It also gives Obama authority to penalize Russian gas giant Gazprom if it is found to be "withholding significant natural gas supplies" from NATO states, or further withholds such gas supplies from Ukraine, Georgia, or Moldova.

The measure would allow Obama to impose financial, commercial and banking penalties on companies or persons he determines have engaged in sanctionable transactions, and deny US entry to violators.