The results, if confirmed by official tallies expected on Monday, would complete a transformation of the government that began in February when President Viktor F. Yanukovych fled after sustained, bloody street protests over his decision to align more closely with Russia.

Expanded power for pro-Western parties is certain to be cheered by the United States and its European allies, which have staked a huge political and financial bet on Ukraine’s ability to emerge from its current crisis as a stable state, and especially to be able to repay its debts.

The United States and European nations are also eager to end the worst violence on the Continent since the conflicts in the Balkans in the 1990s, and to resolve the most dangerous dispute between the West and Russia since the Cold War. That, however, is likely to hinge as much on President Vladimir V. Putin of Russia as on Mr. Poroshenko.

An overwhelming pro-Western majority might also pose a challenge for Mr. Poroshenko as he tries to convince residents of the embattled east that their interests are also a priority in Kiev. Such skepticism is likely to be heightened because of the inability of so many residents of eastern Ukraine to participate in Sunday’s election.

Between the war zone and Crimea, which was annexed by Russia in March, as many as 10 percent of voters might have been prevented from casting ballots, international election observers said. Rebel leaders had recently boasted that they controlled many polling stations in the east, and intended to block the vote.