Gordon Brown warned Hamid Karzai today that he needed to tackle corruption in Afghan politics to keep international support.
During a meeting at No 10 with UN secretary general Ban Ki-Moon, Mr Brown said: "These are important days for Afghanistan when the president is inaugurated.
"We will want him to make clear that he is going to take immediate action on corruption."
Mr Karzai's victory was declared yesterday after Afghanistan's Independent Electoral Commission decided to call off this weekend's second-round presidential ballot, which was triggered by his failure to obtain 50% of votes in an election in August which was marred by widespread fraud.
The ballot had effectively become meaningless following the withdrawal from the race on Sunday of Mr Karzai's only remaining rival, former foreign minister Abdullah Abdullah, who claimed the run-off poll would not be fair.
Mr Brown said Britain wanted to see "a corruption-free government, an inclusive government and a government which will tackle the problem of bringing prosperity to the Afghan people".
He said that if Mr Karzai was successful in tackling these issues and building up the Afghan military and police force, "that will allow British and other troops to come home".
He acknowledged that Mr Karzai faced an "extremely challenging" task and said he looked forward to "further indications" from the President about how he would tackle corruption.
He also offered his condolences to the UN following the death of its staff in a recent bombing attack in Kabul.
He said: "We know that UN staff work in difficult and dangerous situations. Their efforts and their work will never be forgotten."
Asked if international aid would be conditional on seeing corruption eradicated, he said: "We'll only give aid to projects we are sure are going to be delivered."
Setting out the actions he expected the President to take, he said steps should be taken over corrupt officials and district officials must be "free of any stain of corruption".
He said: "What we want and what he (Mr Karzai) now wants is action on corruption, building up the Afghan army and police force and showing that he can bring prosperity to the Afghan people by controlling the drugs trade."
Mr Ban echoed the Prime Minister's sentiments, saying: "I want him (Mr Karzai) to take all necessary measures to meet the expectations of the Afghan people and government and the international community."
He said this would involve ensuring "good governance", eradicating corrupt practices and controlling the drugs trade.
He also urged the returning President to "form a unity government reaching out to all ethnic groups, all political leaders and religious leaders".
He said he had also met Mr Abdullah and urged him to "act as a responsible political leader", who, he pointed out, had won a share of the votes in the first round of elections.
He described the attack on the UN base as "heinous" and thanked Mr Brown for his condolences.
But he said his organisation would not be deterred from supporting the Afghan people and their government.
He added: "Ensuring good governance by eradicating corrupt practices should be a key target for this government and that will be the key to earning trust from the international community."