The caller told Pakistan's President Asif Ali Zardari that India would take military action if Islamabad did not hand over the perpetrators of the Mumbai attacks, the Dawn newspaper said, quoting diplomatic and security sources.
Pakistan responded by putting its air force on high alert and the incident triggered a flurry of intense diplomatic activity, as some world leaders feared the row over the attacks could lead to war.
New Delhi has increasingly pointed the finger at Islamabad over last week's devastating Mumbai siege by Islamic militants in which 163 people died.
The violence, sometimes referred to as 'India's 9/11,' has enraged public opinion and threatened a slow-moving peace process.
Dawn said the caller managed to bypass the standard procedures and was transferred directly to Zardari after introducing himself as Pranab Mukherjee, India's foreign minister.
"Whether it was mere mischief or a sinister move by someone in the Indian external affairs ministry, or the call came from within Pakistan, remains unclear, and is still a matter of investigation," Dawn said.
"But several political, diplomatic and security sources have confirmed to Dawn that for nearly 24 hours over the weekend the incident continued to send jitters across the world."
The report said the that the caller also tried to telephone US Secretary of State Condoleezza Rice, but was not put through.