Wafula Chebukati's comments come in the wake of the resignation of Roselyn Akombe, a senior member of the Independent Electoral and Boundaries Commission, over security fears and alleged partisanship on the board.
"I want to issue a stern warning to the players of both sides to stop intentions to interfere in the process," Chebukati told a news conference.
"Let my commission and I do our job and we shall deliver. Interfere as you have been doing and we will get stuck as a country."
The IEBC chairman called for political leaders to hold a meeting to discuss issues around the October 26 rerun.
The new vote was ordered after Kenya's Supreme Court invalidated the results
of a contentious August 8 election -- which gave victory to incumbent President Uhuru Kenyatta -- following a challenge over irregularities.
Chebukati warned that if the current political crisis is not resolved, the country risks finding itself in a situation "possibly worse" than in 2007 and 2008, when more than 1,000 people died in political violence that turned ethnic in nature.
"If we don't cap this mess, I fear for the future," he said.
Chebukati insisted he had no plans to resign. "The politicians are the greatest threat," he said. "I will not tolerate the threats on my staff any more."
Since the Supreme Court ruling, Kenyatta's main challenger for the presidency, opposition leader Raila Odinga, has pulled out
of the rerun, saying that issues around the way the first election was run have not been resolved
Opposition supporters have clashed with police, and the government has banned demonstrations in certain areas.
Akombe: Not too late to avert crisis
Former commission member Akombe, in a statement issued Tuesday from New York, described the IEBC as "under siege" and said it could not guarantee a credible presidential election next week.
Fellow commissioners had become increasingly partisan, coming to meetings "ready to vote along party lines," she said, and were unwilling to "be frank with the Kenyan people."
Akombe said she had agonized over whether to quit, but had decided to do so because the commission had "become a party to the crisis" and lives were potentially at stake.
"It is not too late to save our country from this crisis," she said. "We need just a few men and women of integrity to stand up and say that we cannot proceed with the election on (October 26) as currently planned."
Akombe highlighted concerns over last-minute changes to election-related technology and results transmission, rushed training of staff because of fears of protest violence and the intimidation of electoral commissioners and staff.
"We need the commission to be courageous and speak out, that this election as planned cannot meet the basic expectations of a credible election," she said.
"Our people are resilient. Our people are patient. What we are faced today is a political crisis that cannot be solved by the commission alone. Let us solve the political crisis we have at hand and then chart the way forward toward a credible presidential election."
In an interview with the BBC
, Akombe said she had received numerous threats while in Kenya and did "not feel safe enough to be able to go home."
Speaking with CNN on Friday, opposition leader Odinga said his coalition did not want to "facilitate another rigging of elections" by taking part in a process in which none of the issues that led to the annulment of the first vote were resolved.
He urged the replacement of some electoral commission personnel, among other changes.
The continued uncertainty has raised fears of wider unrest in the east African nation, which has suffered bloody election-related violence in the past, particularly in 2007-08.
Last week, the government called for a ban on demonstrations in the central business districts of Kenya's three main cities -- the capital Nairobi, Mombasa and Kisumu -- citing security fears.
Police and opposition supporters have clashed in recent days in Nairobi, Kisumu and elsewhere. On October 11, police tried to deter opposition protesters from marching on the headquarters of the electoral commission in downtown Nairobi by firing bullets in the air and releasing tear gas.