"What he told reporters was that the meetings with the United Nations are not important. It's more important for me to be in Afghanistan at this sensitive time."
Meetings at the UN General Assembly were due to start in New York on Tuesday and the developments in Afghanistan were on their agenda.
The UN meeting would have been Karzai's first trip abroad since the presidential election one month ago.
No official election result has yet been announced and there have been widespread allegations of vote fraud.
Preliminary results have given Karzai 54.6 per cent of the vote, enough to avoid a second round runoff against his main rival Abdullah Abdullah, a former foreign minister, who has 27.7 per cent.
But election observers from the European Union have said that up to 1.5 million of the ballots could be fraudulent, leaving open the possibility for a dramatic swing in fortunes if the ballots are annulled after the investigation.
The UN-backed Electoral Complaints Commission (ECC) has ordered recounts at more than 2,500 polling stations, around 10 per cent of the total, after it found "clear and convincing evidence of fraud".