The elections will come ahead of NATO's plans to pull most of its combat troops by end of 2014 when Afghan security forces are to take charge of the country's security.
Karzai, who won re-election in 2009 following charges of massive election fraud, cannot constitutionally seek a third term. His current term ends in mid 2014.
The New York Times reported that Karzai had promised the presidential election would be conducted on schedule since those, including foreign supporters, involved in the process have been saying they don't want to see the same problems as in 2009.
However, the Times, quoting Western officials, said were doubts whether a clean election could be guaranteed in the current climate of violence and official corruption.
The Times said opposition parties also remain concerned about Karzai's threat to veto a proposed law requiring the appointments of two foreigners by the United Nations to the country's five-person Electoral Complaints Commission, which handles electoral fraud issues.
"We are worried that the government might interfere in the elections somehow and turn it to its favor," a spokesman for an opposition alliance told the Times.
The Wall Street Journal said Karzai is widely expected to support a trusted ally to succeed him. It quoted observers as saying they were skeptical a new voting system and electoral law could be completed in time to prevent fraud.
Karzai spokesman Aimal Faizi, however, said the president doesn't have a preferred candidate, the Journal reported.
"He has not named anybody but he has held a series of meetings with different people around the country to create a road map for elections," Faizi said. "It's an inclusive process, not exclusive."