“The prime minister should immediately resign. He should step down without causing further crisis,” Sharif said speaking to a private television channel.
Sharif, who has twice served as prime minister, also called for fresh elections.
“The court verdict is based on truth and reality. It must have punished the prime minister with a heavy heart, but the prime minister himself is to be blamed,” he said.
“The prime minister himself invited this situation,” he added.
The Supreme Court convicted Gilani of contempt on Thursday over his refusal to write to authorities in Switzerland asking them to reopen corruption investigations into President Asif Ali Zardari.
He was given only a nominal sentence, detained until the court adjourned, but could still be forced out of office.