A private volunteer group from Florida said it has launched an attempt to usher about two dozen Americans out of Ukraine in the first evacuation of U.S. citizens since the country came under Russian military attack on Thursday.

The rescue operation by the Tampa-based nonprofit Project Dynamo began in Kyiv as Russian air strikes on the Ukrainian capital were starting in the predawn darkness early Thursday local time, the group's spokesperson, James Judge, told Reuters.

He said the evacuees, numbering 23 or 24 U.S. citizens and legal U.S. permanent residents, met at a pre-determined rendezvous point and left Kyiv in three vehicles bound for an American embassy in an undisclosed neighboring country.

"The evacuation began minutes after our team on the ground physically felt the nearby explosions in Kyiv," Judge said. The convoy stopped for the night late on Thursday local time, and would proceed to its destination in the morning, he added.

Project Dynamo, an all-volunteer, nonprofit group consisting mainly of U.S. military veterans, was founded last August to gain safe passage from Afghanistan for Americans after the Taliban seized power there.

Judge said the group turned to Ukraine in December amid Russia's military buildup and increased rescue preparations in January after the U.S. government warned it would not be in a position to evacuate its citizens should they become trapped by a Russian invasion.

Reuters was unable to immediately verify the organization's account.

But Project Dynamo made headlines in late September when it chartered a flight that evacuated more than 100 Americans from Kabul to the United Arab Emirates. Those evacuees later flew on to the United States. Bryan Stern, a Project Dynamo founder who led that effort, was on the ground in Kyiv coordinating this week's overland evacuation from Ukraine, Judge said.

Stern was shown in a Dynamo-released photograph of 13 people described as part of the Ukraine evacuation group seated in what appeared to be a small motor coach smiling at the camera. A separate photo showed Stern outside the U.S. Embassy in Kyiv.

Most embassy staff were ordered out of Ukraine earlier this month and core operations were shifted to the western city of Lviv, though remaining U.S. personnel have since been sent to Poland until further notice.

Judge said U.S. authorities were being "kept informed of what we're doing, but we're not working in coordination on behalf of them."

Judge said Dynamo has been contacted by "hundreds" of people seeking evacuation from Ukraine for themselves or loved ones since Russian hostilities began.

State Department spokesman Ned Price told a briefing on Wednesday some 6,600 Americans were believed to be residing in Ukraine in October but a precise number as of this week was unknown.

Price said the Polish government was asked to ensure that Americans fleeing Ukraine can enter Poland without advanced authorization, and a U.S. welcome center just across the Polish border would assist any Americans in need.