Police erected metal barriers on 7 August around a tent protest encampment of hundreds of supporters of Tymoshenko, the country's leading opposition politician, who was jailed on Friday after the judge ruled she was disrupting the trial.
50-year-old Tymoshenko, who brought thousands out on to the streets during the 'Orange Revolution' protests of 2004, is the fiercest opponent of President Viktor Yanukovich.
She denies charges by Ukrainian prosecutors that she illegally forced state energy company Naftogaz to sign a gas supply contract with Russia while prime minister in 2009.
After several days of court proceedings in which Tymoshenko refused to stand for the judge and repeatedly accused him of being a puppet of Yanukovich, she was led from the courtroom on Friday and driven to a detention centre under police escort.
Several hundred of her supporters, including several allied deputies from parliament, have been sleeping in tents on Kiev's main thoroughfare in solidarity with her and calling on people to join them.
The United States -- an important backer for the ex-Soviet republic which is drawing on a multi-billion dollar International Monetary Fund credit arrangement -- echoed concern by the European Union at Tymoshenko's arrest.
The "incarceration of former Prime Minister Tymoshenko has raised concerns internationally about the application of the rule of law in Ukraine and further contributes to the appearance of politically-motivated prosecutions," a statement from the US embassy said.
"The US government shares those concerns and urges that Mrs. Tymoshenko's incarceration be reviewed and consideration be given to her immediate release," it said.
In the early hours of Sunday police threw up metal barriers around the encampment but did not prevent people entering or leaving the area. By evening the area was milling with people but there was little sign the protest was attracting much support from city dwellers strolling with their families.
On Friday, EU foreign policy chief Catherine Ashton and EU enlargement commissioner Stefan Füle also criticised Tymoshenko's arrest.
The EU is in talks with Ukraine to strengthen bilateral ties, with the eventual goal of forming a free trade zone.
Tymoshenko, who twice served as prime minister between 2005 and 2010, says the case against her is politically motivated and has been fabricated on the orders of Yanukovich, who only narrowly beat her in last year's presidential election.
She is next due in court on Monday.
The latest developments are casting a shadow on what was expected to be a festive summer in Ukraine, as the country is celebrating this summer the 20th anniversary of its independence. On 16 July 1991 the parliament of the former Soviet Republic adopted the Declaration of the State Sovereignty of Ukraine. A month earlier, a similar declaration was adopted by the Russian Federation.
EurActiv with Reuters