Mutunga, the president of the Supreme Court, said on Wednesday that threats against him and attacks against five judges, including some involving guns, will not be tolerated ahead of the March 4 vote.
Kenyatta and his running mate William Ruto, who form Kenyatta's Jubilee Coalition, are currently facing charges of crimes against humanity brought by the International Criminal Court for their roles in orchestrating violence after the 2007 election, when more than 1,000 people died.
"Let no individual, group, candidate or supporter imagine that cowardly and dark acts such as these will cower us," said Mutunga.
"We have seen and overcome worse, and we will all soldier on for this country. None will be held hostage by a cabal of retrogrades."
He said he suspected a letter threatening "dire consequences" if courts rule against the two candidates' eligibility came from the outlawed Mungiki criminal gang, which was involved in the 2007 violence.
Kenya's High Court last week said it had no jurisdiction to determine whether Kenyatta, the deputy prime minister, and Ruto can run.
Kenyatta, whose father was Kenya’s first president, is accused of financing attacks meted out in 2007 by the Mungiki against supporters of then opposition leader prime minister Raila Odinga, who narrowly leads Kenyatta in opinion polls ahead of next month's election.
Rights groups have sought the courts' help to strike Kenyatta out of the race, saying his integrity was discredited by his trial, but Odinga has said his opponent deserves to face him in a free and fair election.
Kenyatta and Ruto denied their supporters attacked the judiciary, but condemned the threats.
"We condemn in the strongest possible terms, any actions that infringe on the safety, security and capacity for judicial officers to discharge their duties without fear or intimidation," they said in a joint statement.