International Criminal Court (ICC) prosecutors say they do not object to delaying the trials of four prominent Kenyans charged with fuelling violence.
One of the suspects, Deputy Prime Minister Uhuru Kenyatta, is contesting next week's presidential elections.
The ICC trials, over violence that broke out after the disputed 2007 election, was due to start in April.
But defence lawyers complained that they had not been given enough time to prepare for the cases.
ICC spokesman Fadi El Abdallah said judges had not yet decided whether to delay the trials, the Associated Press news agency reports.
But the prosecutors' comment, in written filings posted on the ICC website, makes it likely the trials will be pushed until later in the year.
The prosecution had initially rejected calls for a delay, but now admits that "operational constraints", such as the availability of court space, may make an April date "untenable", reports the BBC's Anna Holligan from The Hague.
The political implications of a delay would be significant, if there is no clear winner in Kenya's 4 March election, our reporter says.
It would mean that the accused would be free to stay for any run-off vote, she adds.
Mr Kenyatta and his running mate, William Ruto, are charged with crimes against humanity over the violence which left more than 1,000 people dead and 600,000 homeless after the 2007 election.
Kenya's former UN ambassador Francis Muthaura and journalist Joshua arap Sang are facing similar charges at The Hague.
They all deny the charges.
About two weeks ago, a Kenyan High Court refused to annul Mr Kenyatta's candidature, saying it did not have the power to do so.
He is a frontrunner for the presidency, along with Prime Minister Raila Odinga, in next week's election.
Mwai Kibaki is stepping down, at the end of his two terms.
Defence lawyers had said they need more time to prepare for the trials because prosecutors had not disclosed all their evidence.
The 2007 violence broke out after Mr Odinga's supporters reacted angrily to Mr Kibaki's victory, claiming the vote had been rigged.
Mr Kibaki was backed by Mr Kenyatta, while Mr Ruto supported Mr Odinga. However, the two have formed an alliance to contest next week's election.