The document allows, in particular, to supply defensive weapons to Ukraine and authorizes the president of the United States to introduce a new package of sanctions against Russia because of its aggression in Ukraine.
"I expect that this will be done before the end of the week," White House spokesman Josh Earnest said.
According to the spokesperson, Obama remains concerned about the bill, but said that the legislation still gives him the necessary flexibility.
It is worth noting that earlier the White House said that Obama has not yet decided whether to sign the bill or not.
Earlier, it was reported that the U.S. Congress passed the "Ukraine Freedom Support Act" bill, which provides for supplying Ukraine with weapons and providing it the status of non-NATO ally.
However, later the White House said that the Act of Congress will not affect the U.S. policy on arms supply to Ukraine.