KIEV, Sept. 1 - Ukraine's parliamentary majority showed signs of cracking Tuesday after a right-wing party said it was leaving the coalition over a measure to give more power to Ukraine's regions, including the rebel-held east.

The announcement from the Radical Party, which came in fifth in last year's election, came as two more National Guard officers died from injuries suffered in a grenade explosion, bringing the death toll to three from Monday's clashes between nationalists and police outside Ukraine's parliament, the AP reported.

About 140 people were hospitalized following the violence, most of them law enforcement officers, the Interior Ministry said.

Most of the 100 violent protesters were members of Svoboda, a Ukrainian nationalist party that holds only a handful of seats in parliament. Wielding truncheons, pipes and sticks with nails, they faced off against police in riot gear.

Investigators have summoned nearly 30 people for questioning including Svoboda leader Oleh Tyahnybok in connection with the clashes, the Interior Ministry said Tuesday. A statement on the website of the Ukrainian president claimed that Svoboda, the Radical Party and one other group were behind the rally Monday.

President Petro Poroshenko met with the country's top law enforcement officers and urged for a speedy investigation into the clashes. Prosecutor General Viktor Shokin said the perpetrators and organizers of the clashes would face lengthy prison terms on charges of carrying out a terrorist attack.

Parliament speaker Volodymyr Groisman urged all political parties Tuesday to condemn violence and rally around the president and his plans to devolve powers, but the Radical Party led by Oleh Lyashko said it would now officially oppose Poroshenko and his plan, which they believe threatens the country's sovereignty.

The decentralization of power was a condition demanded by Russia for a truce signed in February aimed at ending the fighting between Ukrainian government troops and Russia-backed separatists that has left more than 6,800 people dead since April 2014.

Poroshenko has found himself in a tight spot with the bill, attracting the ire of nationalists who accuse him of undermining Ukraine's independence. At the same time, the Russian-backed rebels say the bill does not give them as much as power as they want.

Lyashko, who came in third in Ukraine's May 2014 presidential election, said Tuesday he will demand a referendum to discuss the measure.

"Only the Ukrainian people as a source of power have the right to say what kind of country they should live in," he said in comments carried by Ukrainian news agencies.

A total of 265 lawmakers voted to give preliminary approval to the bill, which still needs final approval. Only three out of the government's five coalition parties voted for the bill.

The government insists the constitutional amendment would devolve powers to local communities in all of Ukraine, from east to west, while making sure that Ukraine stays one state. (ap/ez)