President Barack Obama on Monday admonished President Hamid Karzai of Afghanistan that he must take on what U.S. officials have said he avoided during his first term: the rampant corruption and drug trade that has fueled the resurgence of the Taliban.

As Karzai was officially declared the winner of the disputed presidential election, Obama placed a congratulatory call in which he asked for a “new chapter” in the legitimacy of the Afghan government.

What he is seeking, Obama told reporters afterward, is “a sense on the part of Karzai that, after some difficult years in which there has been some drift, that in fact he’s going to move boldly and forcefully forward and take advantage of the international ...