Ukraine was hoping the European football championship would be a chance to showcase the country and boost its ties with the European Union.
In a visit Thursday to Lithuania, U.S. Senator John McCain joined the chorus calling for Tymoshenko to receive urgent medical care.
McCain also said the Ukraine's leadership cannot expect closer relations with Europe while it persecutes political opponents and fails to hold free and fair elections.
"The message needs to be clear and sent now by the EU to the Ukrainian government," he said, suggesting that international observers could go to Ukraine and arrange for Tymoshenko to leave.
Gary Peach in Riga, Latvia, contributed to this report.