Despite the warm welcome given millions of Ukraine refugees in the European Union since the Russian invasion, EU officials said Tuesday there are some fears of wavering support caused by a slowing economy that especially affects poor families and the creeping influence of Russian propaganda.

According to AP, EU Home Affairs Commissioner Ylva Johansson stressed that support for the 4 million Ukraine refugees being cared for in the bloc is steadfast, but a special report said "what we might call 'solidarity fatigue' is beginning to set in in some member states."

"The cost of living crisis has hit low- and medium-income families in host societies and created a context in which Russian propaganda could be more successful," special EU adviser on Ukraine Lodewijk Asscher said in the report.

Russian President Vladimir Putin "has a huge interest in influencing public opinion on displaced persons from Ukraine. The discourse on migration refugees can be weaponized to sow division within the EU," the Dutch politician said, adding that some of the 27 EU member states have already reported more disinformation campaigns targeting the issue.

Within the EU, a Temporary Protection Directive was issued to make sure Ukrainians could take shelter and receive help with as few strings as possible. Member states have even started building temporary Ukraine "villages" to help the refugees integrate better in society.

However, the report warns that refugees who are torn between seeking shelter and their homes where fighting is taking place suffer from injuries and losses, creating a "waiting dilemma."

It makes "it difficult to decide to start learning a new language, to embark on more serious training or education programs, or to integrate children into the education system of the host country," Asscher said, adding that companies also hesitate to invest in them since they might be gone at short notice.

Overall, Asscher said, "solidarity is alive and kicking. But there is fatigue, especially amongst the more vulnerable refugees as well as the most vulnerable in receiving societies."

Hungary has shown the highest level of support for refugees from Ukraine in Eastern Europe.