In a separate attack the same day, a suicide bomber struck the funeral of a police commander, attended by government officials and a member of parliament, in the eastern province of Nangahar, killing at least 24 people and injuring 68. Authorities said that toll could rise.
The Islamic State (IS) terror group, which has targeted Sikhs before in Afghanistan, claimed responsibility for the attack on the gurdwara in Shor Bazar area at about 07.45 am (local time) as 150 worshippers were inside the building.
The announcement came from Secretary of State Mike Pompeo on Monday after he made an unannounced visit to Kabul to meet with Ashraf Ghani and Abdullah Abdullah. Each has declared himself president of the country after disputed elections last year.
The announcement came hours after the US said its forces had started pulling out of two bases in Afghanistan, in line with a deal signed between Washington and the Taliban in Doha last month aiming to end America's longest war.
The communication ministry is located in downtown Kabul, about two kilometres (1.25 miles) from the green zone.
An Afghan government security source told Reuters that the explosion had taken place on Jalalabad Road in eastern Kabul, near a district that is home to international company and NGO offices.
Washington would seem to be ramping up efforts for a negotiated end to Afghanistan's war.
Later Wednesday, suspected Taliban insurgents overran a security outpost in the northern Badghis province and then ambushed reinforcements, killing a total of 10 soldiers, according to Jamshid Shahabi, a spokesman for the governor.
A security official said the explosions were caused by rockets fired from outside the city, and some fell near the presidential palace, around embassy compounds and government buildings.
Clashes are ongoing and the area is cordoned off by the Afghan security forces.
The assaults underscore growing concerns about security in the lead-up to legislative elections scheduled for October 20, which are seen as a test-run for next year's presidential poll.
Some of the attackers at the Marshal Fahim Military Academy have been killed, an Afghan security source said, adding the gunmen had not managed to enter the academy.
"The latest toll from Kabul hospitals stands at 40 martyred and 140 wounded," health ministry spokesman Waheed Majroh told AFP.
Ministry of External Affairs spokesperson Raveesh Kumar said there was no fire and no casualties were reported in the incident.
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"A rocket landed near the airport this morning. No casualties reported," interior ministry spokesman Najib Danish said in a tweet.
The neighbourhood is home to many Shiite Hazaras, a persecuted ethnic minority which was hit hard just a year ago in a strike which killed dozens - in the first attack claimed by the Islamic State group in the heart of Kabul.
Kabul city was on locked down today with armed checkpoints and armoured vehicles patrolling the streets to prevent a repeat of protests that spiralled into street clashes, leaving at least four people dead.
"In this powerful attack 90 people have been killed and 461 wounded, including many women and children," said the government's media centre, with health officials warning the toll could climb further.
Modi, who is in Spain on a visit, said India stands with Afghanistan in fighting all forms of terrorism.
Sources told CNN-News18 that the bomb went off 50 meters from the Indian mission. All staff members have been moved to strong rooms, sources added.
No group has so far claimed responsibility for the blast, but it comes in the middle of the Taliban's annual summer offensive, which the insurgents are ramping up after a brief lull during the recent holy fasting month of Ramadan.
President Ashraf Ghani condemned the assault "in the strongest possible terms" in a statement from the presidential palace, located only a few hundred metres away from the scene of the blast.
An explosion rocked central Kabul early on Tuesday and a thick plume of black smoke could be seen rising from the vicinity of the sprawling US embassy in the Afghan capital, Reuters witnesses said.
"Bharat Heavy Electricals Limited (Bhel) has commissioned two 220/20kV substations in Afghanistan. The project has been executed by Bhel on EPC basis," the company said in a statement.