Deb also requested Shah for the early completion of a Central Bureau of Investigation (CBI) probe into the murder two journalists in Tripura.
The requests were made during Deb and Shah's meeting in New Delhi on Thursday, the official added.
Within a month of coming to power in March 2018, the Bharatiya Janata Party (BJP)-led state government handed over all the 74 chit fund cases to the CBI to probe the illegal collection of money from people by the unlawful chit fund operators.
BJP spokesman Nabendu Bhattacharjee said in Agartala that the previous Left Front government in the state had, in various ways, backed the unauthorised chit fund organisations and non-banking finance companies (NBFCs) in looting crores of money from gullible people.
"The CPI-M government was averse to handing over all the cases related to chit fund organisations and NBFCs to the CBI," he said.
Bhattacharjee told the media that the BJP government's vision was to free Tripura of corruption and the drugs menace.
The opposition CPI-M leaders strongly refuted the accusations.
CPI-M Central Committee member and Left Front convenor Bijan Dhar said it was widely known that the CBI had been misused by the ruling parties at the Centre.
The erstwhile Left Front government in Tripura had enacted a law in 2000 to deal with illegal NBFCs and chit fund organisations and, since 2016, had began confiscating all movable and immovable properties in the state of the Rose Valley group.
Rose Valley, a Kolkata-based chit fund company, is now under the scanner of the Enforcement Directorate and the CBI, while the company's sole proprietor and Chairman Gautam Kundu and other important functionaries were arrested in Kolkata in 2015.
The Chief Minister during his meeting with Shah also requested him to deploy two battalions of Tripura State Rifles (TSR) outside the state to facilitate to recruite hundreds of unemployed youths.
( With inputs from IANS )