Western-leaning leader Viktor Yushchenko had already vetoed the bill, which turns Ukraine into a parliamentary republic and effectively makes the president a mere figurehead.
But the Supreme Rada overrode the veto with 366 votes last Friday, when a former opposition bloc joined the parliamentary majority, which supports the pro-Russian prime minister, Viktor Yanukovych.
Under the constitution, the president must sign the bill into law within two weeks of its submission by parliament. However, Yushchenko's office said that as the text of the resubmitted bill differed from that passed by parliament in late December, the deadline does not apply.
The president "sent a letter to the Supreme Rada chairman saying the text of the bill on the Cabinet resubmitted to the president for signing differed from the text of the bill parliament passed December 21, 2006," the presidential press office said, explaining that one clause had been removed.
Yushchenko refused to sign the bill on Wednesday, accusing parliament of violating the national unity pact that political leaders signed in August in a bid to end a protracted political crisis in the ex-Soviet state. The document served as a condition for Yushchenko's backing for his former arch-rival Yanukovych as prime minister.
The new law allows the parliamentary majority to nominate a candidate for prime minister, as well as defense and foreign ministers, the latter being the president's prerogative under the unity pact.
Lawmakers also rejected every one of Yushchenko's 42 proposed amendments to the law.
The pro-presidential Our Ukraine party called the document unconstitutional, "threatening the rights and freedoms of Ukrainians," and said the country was witnessing a serious democratic crisis.
The president will make a decision on the bill in due course, the press office said.
