KABUL—Afghanistan's finance minister called for a full investigation of allegations that he took payoffs from the country's largest bank, and another former minister linked to the scandal said he was the target of a political smear campaign.

Kabul Bank nearly collapsed five months ago amid public allegations that its owners used it to make favorable loans to themselves and to politically connected associates, sparking what has become the highest-profile corruption scandal in the nine years since the war in Afghanistan began.

Earlier Afghan Officials Probed Over Bank

People familiar with overlapping Afghan and U.S. investigations into allegations of fraud at the lender say that on top of almost $1 billion in such loans, there is growing evidence the bank's senior executives made tens of millions of dollars in bribes and other payoffs to Afghan officials, including some with close ties the U.S. The payoffs were intended to keep regulators from scrutinizing the bank's books, the people familiar with the investigations say.

Two of the people alleged to have taken payoffs, Finance Minister Omar Zakhilwal and former Interior Minister Haneef Atmar, denied the allegations Wednesday.

Mr. Zakhilwal called for a full investigation by the Afghan Attorney General's office, which is already probing Kabul Bank.

President Hamid Karzai's brother Mahmood holds a 7% stake in Kabul Bank. Mahmood Karzai denies any knowledge of wrongdoing at the bank.

The allegations against Messrs. Atmar and Zakhilwal were reported earlier this week by The Wall Street Journal.

"Because my name has been mentioned in this article, I ask the Attorney General's office to make [the investigation] a priority," Mr. Zakhilwal wrote in a letter sent Wednesday to Attorney General Mohammad Ishaq Alako.

Afghan and U.S. investigators told the Journal that the allegations stem from bank records; from personal records kept by the bank's former chairman and largest shareholder, Sherkhan Farnood; and from information provided by bank insiders and other people with knowledge of the alleged payoffs and loans.

Mr. Atmar, the former Interior Minister, said Wednesday that the evidence against him and some others was fabricated and was being fed to investigators because of their ties to the U.S. and their roles in trying to clean up pervasive corruption in President Karzai's administration.

"They are trying to divert the attention of the Afghan people, of the international community from the real problems," Mr. Atmar said in a telephone interview from Istanbul, where he is traveling.

Messrs. Zakhilwal and Atmar have both had difficult relationships with President Karzai. Mr. Zakhilwal, the finance minister, was quoted criticizing the Afghan leader in a meeting with American officials in 2010, according to a U.S. diplomatic cable leaked by the website WikiLeaks. Mr. Atmar was pushed out in June after spearheading anticorruption investigations into close associates of President Karzai.

Mr. Atmar said Wednesday that he had been forced out because of his work setting up a special investigative unit known as the Major Crimes Task Force, which has won American praise, and his work with an investigation into another financial institution, known as the New Ansari Exchange.

The task force—aided by the Federal Bureau of Investigation, the Drug Enforcement Administration and other U.S. government agencies—led an investigation into New Ansari, an informal money transfer and exchange business.

Before it was raided by investigators just over a year ago, New Ansari was so large that it effectively set Afghanistan's exchange rate. U.S. officials allege that the firm moved billions of dollars on behalf of corrupt officials, the Taliban and drug kingpins, an operation first detailed by the Journal in August.

President Karzai shut down an investigation into New Ansari over the summer after one of his key aides was arrested in connection with the probe. He has since tried to limit the work of the task force.

"I am probably the most hated of all the people that they are accusing at the moment because it was me who" pressed the New Ansari investigation, Mr. Atmar said. "Do you know what they call me in the presidential palace? They call me an American spy."

President Karzai's office and the Attorney General's office didn't respond to requests to comment on Wednesday.

U.S. Embassy spokeswoman Caitlin Hayden said in a statement, "The U.S. Embassy has maintained positive, productive relationships with both Minister Zakhilwal and former Minister Atmar to push forward progress in areas important to the Afghan people. We have seen the recent news articles alleging possible wrongdoing, but we do not respond to allegations. We expect the appropriate Afghan officials will look into the facts and evidence and take the appropriate actions."

Write to Matthew Rosenberg at matthew.rosenberg@wsj.com