Afghans head to the polls in April for provincial council and presidential elections. Kubis said the elections should take place in an atmosphere of peace.
"My message [to the Taliban] directly or indirectly, [is to] allow the people to vote," he said in an interview broadcast Saturday by Tolo TV. "This is their right. These are your people. This is your country as well."
A travel warning issued last week from the U.S. State Department warned the Taliban and other anti-government groups remained active in Afghanistan.
In its annual report, the U.N. Assistance Mission in Afghanistan said "anti-government elements" were responsible for more than half of the estimated 3,000 civilians killed and 5,600 injured in 2013.
"Stop killing civilians," Kubis said.
The Taliban took credit for a January attack on a popular upscale restaurant, which counted four U.N. officials and a representative from the International Monetary Fund among the estimated 21 dead.
International forces in Afghanistan are wrapping up combat operations as national forces take on more security responsibilities.
Notable deaths of 2014 [PHOTOS]