Zahedan, home to many of Iran's minority Sunni Muslims, is the capital of the Sistan-Baluchistan province, which borders Afghanistan and Pakistan.
The region is frequently the scene of clashes between police, armed groups and drug traffickers.
A senior police official was quoted by the Mehr News Agency as saying that the violence is the handiwork of elements trying to unsettle Shia-Sunni relations in the run-up to the June 12 presidential elections.
Sunni Muslims protested and caused some damage to public property in the city on Sunday after rumours circulated that a senior religious leader had been assassinated, Iran's Press TV said.
It said that dozens of civilians were injured during the protests.
Iran partially closed its border with Pakistan on Monday, allegedly in response to the attacks.
The crossing at Taftan was closed for trading but foot traffic was still being allowed through, Oamar Masood, a local government official in Pakistan's Baluchistan border province, said.
He said that no reason had been given for the closure but that the Zahedan mosque bombing "could be the reason".
Three men were hung on Saturday for providing explosives for the bombing and, on Monday, authorities said that they had arrested a number of Sunni and Shias suspected of instigating violence.
A group called Jundollah, or Soldiers of God, claimed responsibility for the mosque attack. The Sunni group has previously been linked to al-Qaeda.
Iran summoned the Pakistani envoy to Tehran in the wake of the Zahedan mosque attack.
Manouchehr Mottaki, the Iranian foreign minister, said Iran and Pakistan had joined forces "in combating insecurity" since Asif Ali Zardari became Pakistan's president late last year.
"A number of rebels detained in Pakistan have been extradited to Iran within this new framework," he said, without specifying whether they belonged to Jundollah.