Official results with 80 percent of the ballots counted give Mr. Yanukovych's party - the Party of Regions - 32.5 percent of the vote.
The commission says the bloc headed by opposition leader Yulia Tymoshenko has about 31.8 percent.
Mr. Yanukovych said on Ukrainian television the results give him the power to form a new Cabinet. But Ms. Tymoshenko says she will ask President Viktor Yushchenko to let her form a new government.
The president's party - Our Ukraine - has about 15 percent of the vote. Ms. Tymoshenko said her party will join with the president's party - a coalition that gives them more seats than the prime minister's party.
However, it is not yet clear if that coalition will have a majority of seats in parliament. Tough negotiations are expected before anyone can form a coalition government.
Mr. Yushchenko and Ms. Tymoshenko were political allies in Ukraine's "Orange Revolution" - the mass protests against the results of the 2004 presidential election that declared Mr. Yanukovych as the victor. Mr. Yushchenko won the revote and named Ms. Tymoshenko prime minister. He later fired her.
Mr. Yushchenko has sought to pursue democratic pro-western reforms. Mr. Yanukovych has stressed the importance of Ukraine's ties with Russia.
President Yushchenko called for Sunday's early elections in April, after dissolving parliament. He accused Mr. Yanukovych of illegally courting members of the president's party to strengthen the prime minister's support in parliament. - VOA News