The campaign for a separate state of Telangana is led by KCR (K Chandrasekhar Rao) of the TRS (Telangana Rashtra Samithi) party.
But within several other political parties, including the Congress, there is no consensus. Representatives from Telangana want a new state. Those from the two other regions - coastal Andhra and Rayalaseema - don't.
In December 2009, a lengthy hunger fast by KCR found huge support, and then Home Minister P Chidambaram, in a surprise midnight announcement, said Telangana would be its own state.
Violent protests in non-Telangana areas and a chorus of criticism by their leaders surprised the Centre. Many parties which had backed the division of the state rescinded their support. The decision to create a new state was suspended.
Last month, representatives of eight parties in the state were invited to Delhi for an all-party meeting. Home Minister Sushil Kumar Shinde promised a decision by January 28.
At the heart of the Telangana dispute is the booming economy of Hyderabad, the capital of Andhra Pradesh. If it is assigned to Telangana, the poorer regions of coastal Andhra Pradesh and Rayalaseema would take an economic hit.
Today's announcement of a deferral led to protests at Osmania University in Hyderabad, which has been the epicentre of the pro-Telangana movement with repeated clashes between the students and the police.
Senior Union Minister Ghulam Nabi Azad said the Centre will consult again with leaders from the three regions of Andhra Pradesh. "There is no deadline, but the talks will be held as soon as possible," he said.
Critics of the central government attribute its indecision on calculations for next year's general elections. Andhra Pradesh, which sends 42 members to the Lok Sabha, will play a starring role in deciding whether the Congress returns to power. 17 of the state's 42 seats are in Telangana
Former Congress leader Jagan Mohan Reddy, who founded his own party in 2011, presents a threat to the Congress, with rallies and local elections proving his surging popularity. Mr Reddy's father, YSR, was chief minister when he died in a helicopter crash in 2009.