They also demanded answers from Christian Turner, the British High Commissioner in Nairobi, over claims of an "abnormally high influx of British military personnel in the country which began around voting day".
Mr Kenyatta, standard-bearer of the Jubilee Alliance, still leads his main rival, Raila Odinga, as counting of votes cast in Monday's knife-edge election continued into a third day on Wednesday.
The number of rejected ballots is becoming crucial to the result, and technical arguments on whether they should be included in final tallies is consuming the increasingly chaotic count process.
"The Jubilee Alliance is deeply concerned about the shadowy, suspicious and rather animated involvement of the British High Commissioner in Kenya's election," Charity Ngilu, joint leader of Mr Kenyatta's coalition and a former government minister.
"The British High Commissioner [has] been canvassing to have rejected votes tallied in an attempt to deny the Jubilee Coalition outright victory."
Mr Turner immediately rejected the allegations on Twitter. "Not true that UK has position/view on rejected votes; that is decision for Kenyans and if necessary Supreme Court," he wrote.
“Claims of British interference, including by the High Commission, in the electoral process are entirely false and misleading," a Foreign Office spokesman said.
"The UK does not have a position on the question of how to handle the rejected votes. That is for the Independent Electoral and Boundaries Commission, and if necessary Kenyan courts, to determine.
“We urge all sides to ensure calm, avoid inflammatory statements, and to take any disputes to the courts.”
British soldiers were currently in Kenya as part of the regular training programme, agreed with the Kenyan defence ministry, the spokesman added.
"This routine exercise is completely unrelated to the Kenyan elections, and was planned nine months ago."
The Ministry of Defence and the British High Commission in Nairobi last week also said the soldiers were there as part ofa training programme.
More than 10,000 British troops pass through northern Kenya to complete their training before deployment. Two battlegroups are currently crossing-over in the country as one completes its exercises and the second arrives to begin them.
Nonetheless, Mr Kenyatta's team called on Mr Turner to "explain to Kenyans the sudden upsurge of British military presence in the country".
Kenya was under intense international scrutiny for this election, following an allegedly rigged ballot in 2007 that sparked six weeks of violence when Mr Kibaki, an ally of Mr Kenyatta, was sworn in.
An expensive new electronic system to send vote counts via mobile phones from polling stations to the national tallying centre failed last night, and the count was continuing manually.
This has raised fears among some Kenyans that opportunities to tamper with the count would rise. The electoral commission, however, said on Wednesday that it was confident in its processes.
Its chairman, Isaak Hassan, promised final results on Wednesday night.
Before the electronic system failed, Mr Kenyatta led Mr Odinga by 53 percent of votes to 42 percent.
Including the rejected ballots in the count would however pull Mr Kenyatta's total below the 50 percent plus one threshold to win without needing to go to a run-off in a month's time.