BRUSSELS—The winner of Sunday's presidential election in Ukraine has told senior European Union leaders he wants some time before committing to a major economic and political deal with the bloc, according to more than a half-dozen officials briefed on conversations.

Officials say they have seen no evidence that incoming Ukrainian president-elect Petro Poroshenko is wavering on the agreement, and they still expect him to wrap it up over the next couple of months. But they say the billionaire chocolate maker has sent the message...