Addressing the Legislative Council, he also said the TDP wanted the centre to review the implementation of the Andhra Pradesh Reorganisation Act and the promises made.
Chandrababu Naidu said that he recalled PM Modi's speech in which he said that "the Congress killed the mother (Andhra Pradesh) by delivering a baby (Telangana)."
The TDP aligned with the NDA hoping that PM Modi would take responsibility for protecting the "mother", the Andhra Pradesh chief minister said, days after pulling out of the BJP-led government at the centre over the special category status issue.
"We reposed faith in Modi but he is not in a position to make it a reality,'" he said in his reply to the motion of thanks to the Governor's Address.
"Hence we are strongly asking him (to honour the promises made in the Reorganisation Act as well as those made in Rajya Sabha by the then Prime Minister Manmohan Singh),"Mr Naidu said.
He also charged the centre with deliberately postponing action on the issue and finding excuses and propagating that he had accepted what the centre had said.
He maintained that special category status was a right of Andhra Pradesh, which was bifurcated to carve out Telangana as a separate state in 2014.
"We are not in the (Central) government but we are still part of the NDA. So I am requesting...Andhra should be immediately granted special category status," the chief minister said.
He asserted that there was "no turning back" as the fight for the state's rights would continue "till we achieve everything that's due."
Referring to Finance Minister Arun Jaitley's "sentiment" remarks, the TDP supremo said Telangana was formed only on sentiment.
"You can't forget that fact. When the state was divided based on sentiment, is it not the centre's responsibility to honour the sentiment now?" he asked.
While explaining the government's stand on the special category demand, Arun Jaitley had said last week that "every state in India has the right to the central fund in the same manner. Sentiment does not decide quantum of funds, it is the constitutional award of the Finance Commission which decides on the quantum of funds that the states get."
He, however, had promised Andhra Pradesh funds equivalent to what a special category state receives and said his government was committed to meeting all promises made to Andhra Pradesh at the time of carving out Telengana.
Referring to BJP leaders' statements that funds for various development works and schemes were coming from the centre, the Chief Minister said that those funds came from people's money.
"That is not your money or our money. It's people's money, paid as taxes. The centre gets more from south India as tax revenue but it spends more in north India," he observed.
The Telugu Desam Party last week pulled out its ministers from the Modi government, but said it would remain a part of the NDA.