Oil and Natural Gas Corp (ONGC) bid for 20 blocks while Oil India Ltd (OIL) bid for 15.
Indian Oil Corp (IOC), GAIL (India) and SunPetro bid for two blocks each, they said.
Reliance Industries-BP made an offer for one block off the east coast.
The block they bid for possibly is the one which BP had demarcated during the expression of interest (EoI) stage.
India had in July 2017 allowed companies to carve out blocks of their choice with a view to bringing about 2.8 million sq km of unexplored area in the country under exploration.
Under this policy, called open acreage licensing policy or OALP, companies are allowed to put in an EoI for prospecting of oil and gas in any area that is presently not under any production or exploration licence. The EoIs can be put in at any time of the year but they are accumulated twice annually.
The blocks or areas that receive EoIs at the end of a cycle are put up for auction with the originator or the firm that originally selected the area getting a 5-mark advantage.
The two window of accumulating EoIs end on May 15 and November 15 every year. EoIs accumulated till May 15 are supposed to be put on auction by June 30 and those in the second window by December 31.
Sources said EoIs accumulated till May 15, 2018 were offered in OALP-II and those that came in by November 15, 2018 in OALP-III. The two rounds ran concurrently.
The government had in January offered 14 blocks in OALP-II bid round and a month later offered another 23 oil and gas blocks and CBM blocks in third round.
Bids for the 14 blocks offered in OALP-II bid round, covering an area of 29,333 square kilometers, were to close on March 12 but the deadline was extended to April 10 and then again to May 15, according to the Directorate General of Hydrocarbon (DGH).
April 10 was also the bid deadline for the 23 oil and gas and CBM blocks offered in the third round, which was launched on February 10. Its bid deadline too was extended to May 15.
OALP-II bid round was delayed by six months and its launch came barely a month before the third round.
Sources said OALP-II and OALP-III ran concurrently.
Oil Minister Dharmendra Pradhan had at the time of launch of OALP-II bid round on January 7 stated that an investment of about Rs 40,000 crore is expected in the prospecting of oil and gas in blocks offered.
In the first round of OALP last year, as much as Rs 60,000 crore was committed in the exploration of oil and gas in 55 blocks or areas.
In the third round, the government is expecting up to USD 700 million (about Rs 49,000 crore) of investment that it hopes will help raise domestic output and cut imports.
The first OALP round was launched in 2017 and bids came in by May 2018. EoIs for second round closed on May 15, 2018, and the blocks were supposed to be put for auction by June but the round was delayed for unknown reasons. OALP-II was finally launched on January 7.
In the meanwhile, EoIs in the third window also closed on November 15, 2018 with as many as 18 blocks and five CBM blocks, measuring 31,722 sq km, being sought for. OALP-III bid round was launched on February 10 with April 10 as the last date for bidding.
Officials said the 14 blocks in OALP-II are estimated to hold in-place resource of 12,609 million tonne oil and oil equivalent gas.
In OALP-1, mining mogul Anil Agarwal-led Vedanta walked away with 41 out of 55 blocks bid out. State-owned Oil India won nine blocks while ONGC managed to win just two.
The 55 blocks have a total area of 59,282 sq km. This compares to about 1,02,000 sq km being under exploration prior to OALP.
Blocks are awarded to the company which offers the highest share of oil and gas to the government as well as commits to do maximum exploration work by way of shooting 2D and 3D seismic survey and drilling exploration wells.
Increased exploration will lead to more oil and gas production, helping the world's third largest oil importer to cut import dependence.
Prime Minister Narendra Modi has set a target of cutting oil import bill by 10 per cent to 67 per cent by 2022 and to half by 2030.
Import dependence has increased since 2015 when Modi had set the target. India imports nearly 84 per cent of its oil needs.
The new policy replaced the old system of government carving out areas and bidding them out. It guarantees marketing and pricing freedom and moves away from production sharing model of previous rounds to a revenue-sharing model, where companies offering the maximum share of oil and gas to the government are awarded the block.