WASHINGTON, D.C. — U.S. Secretary of State Antony Blinken said March 17 that the U.S. is sending an additional $186 million in humanitarian aid to help the more than 3 million refugees who have fled from Ukraine to neighboring countries since Russia attacked the East European nation Feb. 24.

“This brings our total humanitarian aid since last month to $293 million,” Blinken said in a news conference in Washington, while describing the exodus as the “fastest-growing refugee crisis in Europe since World War II — as well as internally displaced people still in Ukraine.”

Ukraine had a population of about 44 million before the conflict began. Those who have been able to escape have fled to neighboring Hungary, Moldova and Poland.

The United Nations High Commissioner for Refugees estimates 6.5 million are internally displaced within Ukraine’s borders. But the situation is expected to deteriorate even more as Russia began attacking Lviv March 18, a city near Poland where many Ukrainians have sought shelter.

“Ukraine’s neighbors in Europe are generously welcoming, supporting refugees. The United States will do our part to help those governments and the humanitarian organizations on the ground meet this tremendous need,” he said.

But he seemed to shy away from saying whether the U.S. would take in Ukrainians.

“There is the refugee referral process, but that takes time,” Blinken answered. “But if people apply for refugee status and seek to come to the United States, of course we will take referrals. But we’re looking at steps that we can take in the near term.”

Of a more than $13 billion package Congress approved for Ukraine, “more than 4 billion of that will go to humanitarian assistance,” Blinken said.

It’s hard to tell whether Ukrainians will end up on the doorstep of the United States seeking refuge, but a Ukrainian family was repeatedly denied entry into the U.S. by Border Patrol agents at the U.S.-Mexico border because of a health measure that keeps migrants out.

The family fled Ukraine via Moldova, then Romania, then boarded a flight to Mexico City. From there they drove to the border seeking refuge near California, where they have family.