Organisers have moved to calm concerns after two new explosive devices were discovered and defused by bomb-disposal teams, one on Thursday in the western city of Uzhgorod and another a week ago in this capital city.
They came a month after around 30 people were injured in four explosions in the eastern city of Dnipropetrovsk for which no-one has claimed responsibility.
While neither Uzhgorod nor Dnipropetrovsk are among Ukraine's four Euro 2012 host cities, Kiev will see a string of games, including the final on July 1.
European football's governing body UEFA remains confident that Ukraine can ensure the safety of the 800,000 foreign fans expected at the tournament, which kicks off on June 8 in co-host Poland.
"We have received full guarantees that security will be ensured," UEFA spokesman Thomas Giordano told AFP.
Viktor Chumak, head of the Ukrainian Institute for Public Policy, said that was a fair assessment.
"The security forces are pretty well prepared to enable the championship to pass off peacefully," he said.
Ukraine has beefed up security but is satisfied that fans will be fine.
"Every single match on our soil is considered a low-risk event," said Markian Lubkivsky, head of the country's organising team, adding that stadia will be equipped with hundreds of security cameras.
"During each game, some 20 security specialists, including police officials and UEFA experts, will keep watch on the situation from a control room," he added.
Private security companies will be responsible for stewarding in Ukraine's four Euro 2012 arenas -- here in Kiev, the western city of Lviv and Donetsk and Kharkiv in the east -- with 4,000 volunteers also having been trained by UEFA, he said.
On top of that, 22,000 police officers will be deployed to keep order during matches, Ukraine's national security office told AFP.
But he acknowledged that Ukraine still faces a shortfall of police dogs and surveillance systems, saying it hopes to cover the gap soon.
There are also persistent fears of hooliganism.
"Hooligans could spark serious public order problems, fights with fans from other countries, and displays of xenophobia and racism," the national security office said.
Since the fall of the Iron Curtain two decades ago, the far-right has found fertile ground among fan gangs in Eastern Europe's football stadiums.
That has become a headline issue abroad after the families of black England players Alex Oxlade-Chamberlain and Theo Walcott said they would not risk going to Ukraine for Euro 2012 after public warnings from the British government.
On Monday, former Tottenham Hotspur and England defender Sol Campbell told a BBC television programme that fans should stay away while the foreign ministries of Euro 2012 qualifiers Denmark and France have also warned about the risk of racist attacks.
Monitors from the UEFA-backed Football Against Racism in Europe (FARE) network have recorded dozens of shocking far-right slogans at Ukrainian league matches, and plan to deploy at Euro 2012 games.
They note that the Euro 2012 spotlight has helped.
"Racism and xenophobia are genuine issues in a number of European countries, including Poland and Ukraine," said Rafal Pankowski of the Polish organisation Never Again, which runs FARE's regional watchdog unit.
"On the other hand, some progress has been made towards eliminating racist behaviour in stadiums, educational activities have been conducted by FARE partner groups targeting teachers and coaches as well as stewards, police and Euro 2012 volunteers in all the host cities," he told AFP.
"In this sense Euro 2012 has served as a positive incentive to tackle racism in the host countries, let's hope the effort continues after the tournament."
Critics underline that a recent attempt to hold a Gay Pride rally here was called off after police allegedly said they could not protect it from skinheads.
"If the Ukrainian police is unable to offer safety to participants in a Gay Pride, then you may doubt whether they can in the upcoming European championships," Dutch lawmaker Marije Cornelissen told the newspaper Trouw.