GENEVA (Reuters) - The United Nations refugee agency said on Thursday that the situation in Ukraine was quickly deteriorating after Russia's invasion and appealed to neighbouring countries to keep their borders open to people seeking a safe haven.

       "We have already seen reports of casualties and people starting to flee their homes to seek safety," Filippo Grandi, U.N. High Commissioner for Refugees, said in a statement.

       The UNHCR said it had stepped up its operations and was working with Ukrainian authorities to provide greater humanitarian assistance. It was also working with governments in neighbouring countries "calling on them to keep borders open to those seeking safety and protection", it said.

       (Reporting by Stephanie Nebehay; Editing by Jon Boyle)