The majority are supporters of liberal opposition candidate Victor Yushchenko, who called on them to encircle the parliament buildings "to help lawmakers" decide on how to handle the scandal-plagued Nov. 21 election results, Itar-Tass reported.
There are so many protesters around the clock where temperatures hover around 25 degrees, neither Yushchenko nor his rival, Prime Minister Vicktor Yanukovich, have been able to reach their offices since Friday, the Novosti news agency said.
The Supreme Court began sifting through more than 10,000 allegations of voter fraud Monday.
Meanwhile, the Moscow Times reports many of the city's police officers have taken to wearing orange ribbons on the sleeves of their navy uniforms as a show of support for Yushchenko.
The Ukrainian Security Service, or SBU, officers have also have expressed support for the opposition candidate. Several addressed a rally at Independence Square Thursday, although an agency spokesman said the service had no partisan position.