In many areas across the country, there were delays, with some skirmishes also reported as contestants accused their opponents of rigging.
Mr Kenyatta admitted to reporters that not enough election materials had been provided.
The primaries are in preparation for August's national poll.
The election will take place nearly a decade after disputed election results fuelled violence that left more than 1,000 dead and 500,000 displaced.
However elections in 2013 passed off relatively peacefully.
Mr Kenyatta said his Jubilee Party had underestimated the number of people who would turn out for the nominations.
"Let us avoid pointing fingers," he said in a series of tweets.
Mr Kenyatta called on voters and contestants to be patient as the party prepared to repeat the vote in the affected areas.
The Jubilee party was holding primaries in 21 out of the 47 counties on Friday, most of them party strongholds.
Nominations in the capital Nairobi had already been pushed back to Monday. The remaining counties will nominate their candidates on Tuesday.
Parties must hold their primaries by Wednesday, the election authorities have said.
Last week, similar polls for the opposition Orange Democratic Movement led by former Prime Minister Raila Odinga witnessed violence, particularly in the western Kenya region.
Mr Kenyatta is seeking a second term in office.
He is being opposed by a coalition of opposition parties known as the National Super Alliance, which is expected to announce its presidential candidate next week.