Mr. Singh is the first prime minister to visit the glacier and Sunday he told the troops stationed there he hoped to transform the world's highest battleground into a mountain of peace.
India and Pakistan have been fighting over the uninhabited glacier for more than 20 years. The Indian army occupied the frigid heights in 1984.
A 2003 cease-fire has stopped the violent clashes but cold weather and altitude sickness continue to kill soldiers on either side.
Retired Pakistani General Talat Masood says ending the fight over Siachen is a key test of both countries' commitment to resolving the broader dispute over Kashmir.
But after a series of failed negotiations, most recently last month in Islamabad, General Masood says neither side appears willing to compromise.
"It has been like that for so many years. It is a question of national ego and determination," he said.
Pakistan wants the glacier demilitarized. However, India says its troops will stay where they are but has promised to not to take any aggressive measures.
India has generally avoided any moves that would suggest a willingness to redraw the existing line of control, not just on Siachen, but throughout Kashmir.
Mr. Singh is completing a three-day tour of Indian controlled Kashmir, the cause of two of the three wars between the nuclear-armed countries.
Sunday, the Prime Minister again ruled out any changes to India's borders. He said the issue was one of security and national prestige.