The offer was made by the new President Ashraf Ghani and was addressed to Mullah Zaeef, the former Taliban ambassador to Pakistan, who has been living relatively openly in Kabul for several years, Wakil Muttawakil, the former Taliban foreign minister, and Ghairat Baheer, a close relative of Gulbuddin Hekmatyar, whose forces are allied with the Taliban.
The BBC says there have also been negotiations to consider appointing Taliban governors to three southern provinces — Nimruz, Kandahar and Helmand.
Quoting a source close to the Taliban's leadership, the BBC says the proposal has been turned down because of the security deals signed by the new government, which allowed some international troops to remain in Afghanistan after combat troops left at the end of 2014.
The Taliban also want changes to the constitution and immunity from prosecution before they would consider entering negotiations on joining the government.
