Kerry's visit came as Kabul desperately tries to bring the insurgent group back to the negotiating table to end their conflict which began in 2001.
Several explosions rang out in central Kabul on Saturday, shortly after the US Secretary of State John Kerry left the Afghan capital following an unannounced visit to call for the Taliban to re-enter peace talks.
Authorities were not immediately able to comment on the nature of the blasts nor on whether they had claimed any casualties, but Taliban insurgents frequently attack government and military installations in the city.
"We heard several explosions, but we don't know what caused them," a police official told AFP on condition of anonymity.
Kerry's visit came as Kabul desperately tries to bring the insurgent group back to the negotiating table to end their conflict which began in 2001.
Buoyed by a series of victories on the battlefield, the Islamist group have so far refused to talk until their conditions are met, including the departure of 13,000 foreign soldiers from Afghanistan.
"We discussed our shared goal of launching peace talks with the Taliban," Kerry told reporters at a joint press conference with Afghan President Ashraf Ghani in Kabul.
"We call on the Taliban to enter into a peace process, a legitimate process that brings an end to violence," he continued, saying: "Of course there is hope for peace." Kerry also added that in July, "NATO allies and partners will gather in Warsaw in order to consider the next round of assistance for the Afghan National Defense and Security Forces."
Another meeting is also scheduled this October in Brussels to review development aid to Afghanistan.
Kerry later flew out of Kabul for the next step of a tour that has so far included Iraq and Bahrain.
Afghanistan, the US, China and Pakistan had formed a four-way group to try to jump-start the talks that were first held in Islamabad last July but fell away after it emerged later that month the Taliban's founder Mullah Omar was dead, leading to infighting within the group.
President Ghani backed Kerry's call, adding: "Peace is the vital need for the nation and the government of Afghanistan and the United States of America -- especially you -- have always been our partner in creating a peaceful atmosphere and regional stability."
"I would like to thank you for the consistent sacrifices and the support of the United States of America. Thousands of your countrymen, your sons and young Americans have given their lives in Afghanistan," he said.
Kerry's first port of call was NATO headquarters, where he met with General John Nicholson, the newly appointed head of the alliance's Resolute Support mission, and US troops.
The US currently has about 9,800 soldiers in the country who have been officially limited to a training and advisory role since the end of their combat mission in 2014.
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