More than 2.5 million Ukrainians have returned to their country since Russia invaded, border police have said.
EU border agency Frontex said more people were heading into Ukraine than out at the moment.
The number of refugees arriving in Poland has slowed to about 145,000 over the past week, almost as many as were crossing every day at the height of the evacuation in March.
By contrast, 163,000 Ukrainians went back over the several land crossings from Poland and entered their home country in the first week of June.
People returning to Ukraine are not necessarily staying for good. UN officials have described people going back and forth for various reasons, including visiting families, checking their properties and helping others to escape.
The total number of crossings from Ukraine passed seven million this week, although that could include several arrivals by the same people. About 3.8 million of those crossings were at the Polish border.
EU countries eased immigration rules in March to grant Ukrainians automatic one-year residency in the bloc, but some have said they would rather go home as the war drags on past the 100-day mark.
Despite the slowdown in departures from Ukraine, pressure on Polish and Romanian crossing points remains high because they are being used to transport desperately needed grain stocks out of Ukraine after Black Sea ports were blocked, Frontex said.
This is made more complicated by the fact that EU and Ukrainian railways have different track widths and grain wagons have to be unloaded or have their wheels replaced.
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A Ukrainian refugee waits to be given shelter in Amsterdam, the Netherlands. AFP -
Campaigner Rend Platings, right, embraces her Ukrainian best friend Kristina Korniiuk as they are reunited outside her home in Cambridge. Ms Platings went on hunger strike until MsKorniiuk's UK visa was approved and painted her house in the colours of the Ukrainian flag. PA -
Ukrainian women attend a job-seekers' meeting aboard the 'Mediterranee' ferry, where they are living while it remains docked in Marseille, southern France. AFP -
Refugee schoolchildren are given Ukrainian primary school education in Berlin, where they also have the choice of attending German schools. Getty -
Teacher Katja with Artem, Sofia and Alexander, refugee schoolchildren who are receiving Ukrainian curriculum primary school education in Berlin, Germany. Getty -
Ukrainian refugee Alikhan Yusupov, 10, on his first day at Caldecote Primary School after his family fled their home in Kharkiv and moved to Cambridgeshire, England. PA -
Roman Starkov plays with nephew Alikhan as they settle into their new home in Caldecote, near Cambridge, after they fled Kharkiv. PA -
Ukrainian refugee Egor Svichkar, 3, whose family now live with a British host. PA -
Ukrainian refugees Yaroslav Kryvoshyia and Irina Kryvoviaz, with her son Sasha as they settle into their new home in North Moreton, Oxfordshire. PA -
An Ukrainian refugee woman sews in Strasbourg, France, part of project for Ukrainian refugees to find jobs after fleeing the war. AFP -
Ukranian refugee Karolina, 16, laughs as she prepares for a party at the La Ville-aux-Dames camp site, her family's temporary home in La Ville-aux-Dames, central France. AFP -
Ukrainians queue outside a refugee centre in Paris. AFP -
Myroslava Perevalska (R), an artist who fled Kyiv, helps a Ukrainian girl paint Easter eggs in Berlin. Getty Images -
The 'Beacon of Ukraine', a gathering at Markthalle Neun in Berlin, bringing together refugees and NGOs as well as showcasing Ukrainian culture. Getty Images -
Larysa Biachenko, 40, who does not know if her house in Chernihiv is still standing, and Svitlana Lykhonos, 43, who was the owner of a hotel restaurant in Frankiusk, peel onions at a special cooking course run by the regional government to offer them a job opportunity, in Alicante, Spain. Reuters -
A convoy of Ukrainian refugees who left Mariupol, accompanied by 17 volunteers, arrive at Juan Carlos I park in Madrid. EPA -
Ukrainian refugees, who arrived in Italy from Lviv after two weeks of travel, are tended to in the reception centre of the Red Cross in Settimo Torinese, near Turin. EPA
Frontex said it had stationed about 350 officers along the Ukrainian border, including in Romania and non-EU member Moldova, to “support evacuation corridors” for refugees.
Western Ukraine is home to more than 1.5 million people displaced in their own country by the conflict. The area has been spared the worst of the fighting but has been pounded by Russian missile strikes.
About 29,000 people crossed into Romania in the first week of June, compared to 30,000 who went the other way. The same pattern was true of Slovakia.
However, an exception was Hungary where arriving Ukrainians continued to slightly outnumber returnees.
Many others are displaced in southern and eastern Ukraine, where hundreds of thousands of people fled the port of Mariupol during a weeks-long Russian siege.
The UN says women and children account for 90 per cent of those who have fled abroad, with men aged 18 to 60 eligible for military service and unable to leave.
