The announcement was however hailed by proponents of an united Andhra Pradesh.
"The consultation process on Telangana issue is on. It may take little more time to reach a final decision," union Home Minister Sushilkumar Shinde said in a brief statement in the national capital after it appeared certain that the Jan 28 deadline set by him to decide on the issue would be missed.
The minister Monday flies to Dhaka to sign the India-Bangladesh extradition treaty.
At an all-party meeting Dec 28, Shinde had said the government will decide on the issue within a month.
"More consultations are needed on the issue," said union Health Minister and Congress leader Ghulam Nabi Azad Azad, who is in charge of Andhra Pradesh.
Azad said Andhra Pradesh Chief Minister Kiran Kumar Reddy, state Congress chief Botsa Satyanarayan and senior state leaders from all regions of the state to Delhi for further consultations.
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"It was for the union home ministry to fix a real time-limit for a decision on the vexed issue," he said.
The BJP accused the Congress of "betrayal" saying it was "playing with the sentiments" of the people of Telangana.
"This is nothing but betrayal. The will of the people of Telangana who are protesting in a democratic and sane manner is not being respected. The Congress and centre are making the whole process a mockery," BJP spokesperson Prakash Javadekar told reporters in Delhi.
Accusing the Congress of once again betraying the people, the Telangana Rashtra Samithi (TRS) decided to launch an agitation targeting Congress ministers, MPs and state legislators in the Telangana region.
TRS leader K. Tarakarama Rao demanded resignation of all Congress MPs and ministers to pressurize the central government to concede their demand.
Leaders of Telangana Joint Action Committee (JAC), which launched two-day protest in Hyderabad Sunday, the BJP, Communist Party of India (CPI) and Telangana leaders of Telugu Desam Party (TDP) condemned the statements of Shinde and Azad.
Hundreds of Telengana activists gathered after police granted permission to the Telangana JAC to hold demonstrations in the Andhra capital till Monday.
There were mixed reactions to their statements from the Congress leaders in Telangana. Some MPs said they were disappointed but hoped that the centre would soon take a positive decision. "We will meet to chalk out our future course of action," said S. Rajaiah, one of the MPs.
State minister K. Jana Reddy was hopeful that despite the delay, Congress would take a decision in tune with the aspirations of the people of Telangana.
Congress leaders from Seemandhra (Rayalaseema and Andhra regions), who were actively lobbying against the state's division, hailed the central government's announcement. State minister G. Srinivasa Rao said it was clear from Shinde's statement that the state would remain undivided.
Shinde's announcement came a day after the Congress core group including party chief Sonia Gandhi and Prime Minister Manmohan Singh discussed the issue Saturday with Shinde, Azad and Gandhi's political secretary Ahmed Patel.