There is no thought of celebrating International Women's Day for the refugees arriving in the Polish border city of Przemysl after leaving their husbands and sons behind to fight in Ukraine.

"We lost our life, our safety," said a dazed-looking Anastasia Kazankina, a lawyer, speaking in a car park outside a busy refugee centre that was once a Tesco supermarket.

"We cannot plan any future because we don't know what will be tomorrow," said Kazankina, clutching her son Ilya's hand and her dog Marsia's lead.

Kazankina, who comes from the capital Kyiv, said she planned to stay in Poland but had no idea what to do there while her husband joins the army.

More than two million people have left Ukraine since the Russian invasion began on February 24.

Over a million have ended up in Poland, with many crossing into Przemysl from the western Ukrainian city of Lviv through the Medyka border control.

I really hope to come back

In the Przemysl car park, buses come and go, spilling out mostly women and children hoping for safety and concerned about those they left behind.

One of the buses is headed to Estonia.

Kyiv grandmother Vera Verozub could be seen pushing her way towards it clutching two heavy bags, helped by her grandsons aged four and 14.

Their parents stayed to "defend the country".

"We took a train to Lviv. From Lviv, we took the bus for a bit and then walked," she told AFP, her teary eyes peeking out of a red hood and a beanie on a chilly morning.

Nearby, Anna Martynova, a retirement home assistant from southern Ukraine, stood on the side with her two children after spending a part of their trip on a bus with no seats.

"It was tough, we've been travelling for two days. There are disruptions, our railway is destroyed, the road bridges are destroyed, " she told AFP.

Martynova is one of the lucky ones -- her husband is already living in Poland, working on the railway.

But soft-spoken Yulia Sokolovskaya said she had to leave her spouse when she left their heavily shelled hometown of Kharkiv with her seven-year-old son.

"In Ukraine, we spent some days in the subway because it was dangerous to go outside," she told AFP.

She hopes to go and stay with friends in Italy -- "a good place to rest" -- but the sunny prospect crumbles as soon as she recalls her husband who had to stay.

"He cannot leave the country, he's still there. I check every hour if he's fine," she said, breaking into tears.

"I left all my life there and I really hope to come back one day."