KABUL, Afghanistan — For almost a year, Taliban leaders in Afghanistan have consistently rejected calls for a cease-fire by officials working to negotiate peace. So a group of grass-roots Afghan activists is going to try asking them in person.

Members of the People’s Peace Movement have been walking across Helmand Province in southern Afghanistan since Thursday, when they left the provincial capital of Lashkar Gah. They are heading toward territory controlled by the Taliban. Most of them were fasting during the day for the Muslim holy month of Ramadan while enduring 100-degree temperatures.

During their 100-mile journey to the district of Musa Qala, which has been under Taliban control for years, they stopped at villages where they were welcomed by crowds who echoed their calls for an end to the conflict in Afghanistan, its latest chapter since the United States invasion.

The activists are on the move as peace talks between the Taliban and the United States seem stuck. But it appeared unlikely that they will get a better reception than the politicians in their pleas for a cease-fire.