But as the two sides struggled to revive a peace process on Monday, Indian foreign ministry spokesman Navtej Sarna added a note of caution.
He said Muslim fighters must be stopped from crossing into Kashmir to join a bloody revolt against Indian rule if any ceasefire was to last.
Outlining India's answer to Pakistani Prime Minister Zafar Allah Khan Jamali's Sunday offer, Sarna told a news conference: "We will respond positively to this initiative.
"However, in order to establish a full ceasefire on a durable basis, there must be an end to infiltration from across the Line of Control."
UN Secretary-General Kofi Annan welcomed both Pakistan's offer and India's response and said he was willing to assist in any way the parties considered "mutually beneficial".
"He urges the two countries to continue these efforts with patience and resolve," a UN statement said.
The nuclear rivals came close to war over Kashmir last year and are struggling to improve relations.
India accuses Pakistan of helping guerrillas cross into Jammu and Kashmir, its only Muslim-majority state, to join a separatist revolt there. Islamabad denies this.
Pakistani PM Zafar Allah Jamali launched the ceasefire initiative
"India has said repeatedly that the infiltrators are able to infiltrate with ease into Kashmir because the Pakistani army provides a cover through the barrage of military fire," Foreign Minister Mian Khurshid Mahmood Kasuri told reporters in Islamabad.
"Now if Pakistan is willing to stop the firing, what does it prove? It proves Pakistan's good intentions - that we have no desire to infiltrate. India should welcome it whole-heartedly without any reservation."
Jamali said Pakistan would order its troops to stop firing from Wednesday, which Pakistan is designating as start of the Muslim festival of Eid al-Fitr, which marks the end of Ramadan.
Troops from both sides regularly exchange artillery, mortar and small arms fire, killing many civilians. Thousands more have been driven from their homes, spending years in makeshift camps or moving in with relatives.
ٍSarna said India wanted to take the peace process further by proposing a ceasefire in the Siachen glacier and the surrounding tangle of mountains where South Asia, Central Asia and China collide.
India and Pakistan have been battling for control of the Siachen glacier, where troops fight on heights above 5500m, since 1984.