KIEV, Ukraine — At least one police officer died and about 50 others were wounded on Monday in violent demonstrations here during a contentious vote in Parliament to grant autonomous status to two rebel-controlled zones in eastern Ukraine.

As Parliament moved to approve the concessions, which were fiercely opposed by Ukrainian nationalists but demanded by Russia under a peace process for the two regions, parts of Donetsk and Luhansk, protesters outside the building scuffled with the police.

Several loud explosions were heard, and although it was not immediately clear how the officer had died, local news media reported that a military hand grenade had been thrown into the police line.

President Petro O. Poroshenko conceded the constitutional change to President Vladimir V. Putin of Russia during cease-fire negotiations in February in Minsk, Belarus, when thousands of government soldiers were surrounded in a battle with pro-Russian rebels in eastern Ukraine.

The chamber approved the constitutional amendment in a first reading, with 265 lawmakers in the 450-member Parliament voting in favor of the so-called decentralization bill during a raucous session. To alter the Constitution, the amendment requires approval from a supermajority of 300 in a second vote.

Supporters of the change say that granting special status to the eastern regions would co-opt a central element of the rebel cause and blunt the drive for separatism.

But the conflict with pro-Russian separatists has angered Ukrainians to such an extent, opinion polls have suggested, that members of Parliament are struggling to win support from voters for any concession to Mr. Putin.

“They are trading in our blood and our corpses,” said a veteran of the conflict in the east, Volodymyr Natuta, referring to members of Parliament who supported the measure. “They sold out Ukraine.”

After the explosion, the police carried a dozen or so bloodied and apparently gravely wounded colleagues to ambulances, with the mayor’s office later reporting that one officer had died.

It was the first death in politicized street violence in the capital since the 2014 uprising, which overthrew a pro-Russian president after months of protests.