0431 GMT June 24, 2018
The amendment was heavily criticized by the opposition, whose legislators boycotted the vote, according to Reuters.
Opposition leader Raila Odinga withdrew from a repeat presidential vote scheduled for October 26 on Tuesday, citing concerns over fairness and transparency. The law must now be signed by the president.
Odinga said his withdrawal would give the electoral commission enough time to introduce reforms that will help deliver a more credible election, BBC wrote.
The Supreme Court annulled the result of the original August 8 poll, which saw Uhuru Kenyatta declared winner, after finding irregularities.
But Kenyatta says he is ready to proceed with the new vote as planned.
The country's electoral commission said Kenyatta had won the August vote by a margin of 1.4 million votes or 54 percent of the total, compared to Odinga's 44 percent.
The election re-run was due to take place on October26, but Odinga said on Tuesday: "We have come to the conclusion that there is no intention on the part of the IEBC [electoral commission] to undertake any changes to its operations and personnel... All indications are that the election scheduled for October 26will be worse than the previous one."
As a result, he said, "considering the interests of the people of Kenya, the region and the world at large" it was best that he withdrew from the race.
Odinga's coalition party believes the election will have to be cancelled as a result of his withdrawal, allowing "adequate time to undertake the reforms necessary to conduct an election that is in strict conformity with the constitution, the relevant laws and the constitution".
But Kenyatta, speaking at a rally in the southern town of Voi, said: "We have no problem going back to elections. We are sure we will get more votes than the last time."