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.