The decision on Lal Krishna Advani's meeting with Maulana Abbas Ansari, chairman of the All Parties Hurriyat Conference, was taken during a two-hour meeting on Wednesday of the Cabinet Committee on Security chaired by Prime Minister Atal Behari Vajpayee.
The government had previously refused to talk directly to Hurriyat leaders.
"The deputy prime minister will meet Ansari in response to his statement of 25 August that they (the Hurriyat) are interested in talks with the government," Home Secretary N Gopalaswami told reporters in New Delhi.
The date and venue of Advani and Ansari's meeting are still to be fixed, he said.
Reacting, Ansari said he welcomed the announcement. "We have always been stressing talks to resolve the issue of Kashmir," said Ansari, who is currently in Delhi.
"We will sit and discuss the offer," he said, adding he would immediately return to Kashmir for a Hurriyat executive council meeting on Thursday.
But he said the Hurriyat would like to know the agenda for the government talks before he met Advani.
Former Hurriyat chairman Abd al-Gani Bhat also welcomed the announcement and said a formal response would be devised by Hurriyat in a day or two.
"We will sit and discuss the offer"
Maulana Abbas Ansari
Chairman, All-Party Hurriyat Conference
Separately, Foreign Minister Yashwant Sinha said talks with the Hurriyat were part of India's "internal process" and had nothing to do with relations with Pakistan.
The Hurriyat wants a resolution of the Kashmir dispute through three-way talks involving India, Pakistan and the separatists.
The Indian government decision comes as the Hurriyat, an amalgam of 27 separatist parties, is itself in crisis with bitter divisions among its leaders.
Six weeks ago the alliance unofficially split, with the pro-Pakistan separatist leader Sayyid Ali Gilani forming a parallel group. Gilani said Ansari, who was elected in July, had no authority to lead the Hurriyat.
A Muslim anti-Indian movement, which New Delhi says is backed by Islamabad, has claimed more than 38,000 live in Kashmir since 1989, according to Indian figures. Separatists put the toll at between 80,000 and 100,000.
Pakistan insists it only provides moral and diplomatic support to separatists it regards as freedom fighters engaged in a struggle for self-determination.
The neighbours have fought two of their three wars over Kashmir - a scenic Himalayan region divided between them and claimed in full by both.