A third member of Ukraine's national guard has died from injuries after Monday's violent protests outside the parliament in Kiev, officials say.
The clashes - involving nationalists - erupted after MPs gave initial backing to reforms granting more autonomy to rebel-held eastern Ukraine.
The first death was reported after a grenade was thrown by a protester.
A ceasefire agreed between Ukrainian government troops and the pro-Russian separatists is reported to be holding.
Violence had escalated in the eastern regions of Donetsk and Luhansk in recent weeks, but the two sides agreed last week that from 1 September all violations of a February truce would cease.
A day after the clashes in Kiev, the government said it was boosting security in the capital, deploying 2,000 police and national guards on the streets and an armoured vehicle on four key routes in the city centre.
About 140 people were injured in Monday's violence, more than half of them national guardsmen.
The protest was organised by the populist Radical Party and ultra-nationalist Svoboda (Freedom) party - who oppose any concession to the separatists.
Police have detained about 30 people suspected of involvement, including a Svoboda member who confessed to throwing a grenade. The suspect was identified as Ihor Humeniuk.
Police say they will question Svoboda leader Oleh Tyahnybok and his top Svoboda colleagues.
Meanwhile, the Radical Party has pulled out of the ruling coalition and joined the opposition MPs in parliament.
The violence erupted after a rowdy parliamentary debate, and a first-reading vote to back the decentralisation bill.
The bill grants more powers to rebel-held areas of Donetsk and Luhansk - a key condition in the Minsk ceasefire agreed with Russia and the rebels in February.
Initially, there were only minor clashes outside parliament, but later small explosions and a much larger one later on - from a grenade.
Addressing the nation late on Monday, Ukrainian President Petro Poroshenko said the violence was "a stab in the back".
Svoboda accused the national guard and police of attacking the protesters, saying this had triggered the clashes.
During the summer, fighting between Ukrainian army forces and the rebels has escalated. But the two sides agreed last week to halt the violence on 1 September, the day children in the region return to school.
"As of 11:00 (08:00 GMT) 1 September 2015, both sides are fully respecting the ceasefire," said Dariia Olifer, a spokeswoman of former Ukrainian President Leonid Kuchma.
Mr Kuchma is a member of the so-called Minsk Contact Group tasked with defusing the Ukraine crisis.
Almost 7,000 people have died since the conflict in eastern Ukraine erupted.
The separatists seized large swathes of the eastern Donetsk and Luhansk regions in April 2014, a month after Russia annexed Ukraine's southern Crimea peninsula amid international condemnation of the move.
Moscow denies accusations by Ukraine and the West that its arms the rebels and sends Russian regular troops across the border, although the Kremlin admits that Russian "volunteers" are fighting alongside the rebel force in Ukraine.