She told a public rally here also addressed by Prime Minister Manmohan Singh that Indian democracy had the strength to overcome conflicts through dialogue.
The rally was held shortly after Manmohan Singh inaugurated a key rail link between the Kashmir Valley and the Jammu region.
"The people in Kashmir are fed up with violence. They want peace and development.
"The large turnout of people during the Panchayat elections in the state is a proof of the people's desire for peace and development.
"I know very well that painful incidents happen here occasionally, but our democracy has enough scope to sort out issues through dialogue and negotiations."
Gandhi said the "hardships faced by the people of the state during the winter months are now a thing of the past.
"Today's inauguration of the all-weather link between Jammu and the valley is a part of the UPA's (United Progressive Alliance) commitment to the peace and progress of the people here."
Gandhi said the National Conference-Congress government in the state had done commendable work in the last five years.