The mosque is in a strict security zone, and an investigation is underway into how the terrorist got there.
The attack, one of the bloodiest in Pakistan in recent years, resulted in many casualties and injuries.
The Pakistani Taliban has officially denied involvement, but the commander of the group, which the militants say has broken away from the group, said earlier.
In the past, the Pakistani Taliban have refrained from claiming some attacks on mosques, schools or markets because they have said they are fighting security forces and not the Pakistani people, but many question their denials.
On Tuesday, rescuers tried to reach worshipers buried under the rubble, pulling out nine people alive, but finding another 24 bodies. According to local officials, no one remained stranded.
“Terrorists want to create fear by attacking those who are doing their duty to protect Pakistan,” Prime Minister Shehbaz Sharif said. He declared a national day of mourning.
The BBC saw ambulances coming and going from the compound every few minutes.
A hospital spokesman confirmed that more than 100 people remain injured, some of them in a critical condition. Meanwhile, the funerals of more than 20 policemen were held, their coffins draped with the Pakistani flag.
The bodies of the dead began to be returned to their relatives.
Between 300 and 400 police officers were in the area at the time, Peshawar Police Chief Muhammad Ijaz Khan told local media earlier.
The mosque is located in one of the most controlled areas of the city, which includes the police, intelligence and counter-terrorism headquarters. On Tuesday, local media lined the road outside the gate – as close as security measures would allow.
Mr Sharif said those behind the attack had “nothing to do with Islam”. He added: “The entire nation is united against the threat of terrorism.”
The Pakistani Taliban – a breakaway group from the Taliban government in Afghanistan – ended a ceasefire in November and violence has been on the rise in the country since then.
Watch: Chaotic scenes inside a mosque after an explosion killed at least 87 people
In December, he targeted a police station like the one in Peshawar, in the northwest of the country which led to the death of 33 militants.
Monday’s blast occurred around 1:30 p.m. (08:30 GMT) during afternoon prayers in the northwestern city, which is near the country’s border with Afghanistan.
An entire wall of the building collapsed and the mosque was covered in bricks and debris as people climbed over the debris to escape.
Hours after the blast, BBC News saw the facility full of wounded, many still in police uniform.
Some were covered in burn cream, their skin red with burns from the explosion. Others have broken bones from being hit by shrapnel.
One man said he still can’t hear because of the sound of the explosion. Another man said he was rescued after spending almost an hour under the rubble.
The Prime Minister went to Peshawar on an emergency visit, where he will receive a briefing from local officials and visit the injured in the blast.
UN Secretary-General Antonio Guterres condemned the attack, and his spokeswoman said: “It is particularly appalling that such an attack took place in a place of worship.”
The attack on the mosque came at the start of a key week for Pakistani diplomacy.
United Arab Emirates President Mohamed bin Zayed Al Nahyan was due to visit Islamabad on Monday, although the trip was canceled at the last minute due to bad weather.
A delegation from the International Monetary Fund is due to visit Pakistan on Tuesday as part of the loan process to prevent the country from defaulting.
In March last year Peshawar became the object of another explosion which killed dozens of people at a Shiite Muslim mosque in a country where the majority of Muslims are Sunni.
In the capital, Islamabad, police declared a heightened level of alert and said that security at all points of entry and exit to the city had been increased.
