On the Multi Commodity Exchange, crude for June delivery went up by Rs 43, or 1.07 percent, to Rs 4,079 per barrel in a business turnover of 19,049 lots.
Brent crude futures were down 38 cents, or 0.5 percent, at $71.80 at barrel by 0219 GMT, having risen 21 cents on Tuesday.
Reliance in the 2018-19 fiscal year that ended March 31, reported a turnover of Rs 6.23 lakh crore. In comparison, IOC posted a turnover of Rs 6.17 lakh crore for the fiscal, according to regulatory filings by the two companies.
Iranian exports have become more opaque since US re-imposed sanctions in November after pulling out of a 2015 nuclear accord between Tehran and six world powers.
US sanctions on Iran have cut the OPEC member's crude exports further in May, adding to supply curbs resulting from an OPEC-led pact.
The IEA, which coordinates the energy policies of industrial nations, said Washington's decision to end sanctions waivers that had allowed some importers to continue to buying Iranian crude added to the "confusing supply outlook."
US sanctions on Iran and Venezuela, disruptions of Russian oil flows in Europe and maintenance at oilfields in the Atlantic Basin and Asia have tightened global supplies and boosted Asia's demand for spot cargoes, they said.
Globally, oil prices gathered steam as investors pinned hopes on renewed prospects of breakthrough in Sino-US trade talks.
India shipped in about 277,600 barrels per day (bpd) of oil from Tehran in April, down about 31.5 percent from the previous month.
According to PPAC, India spent $111.9 billion on oil imports in 2018-19, up from $87.8 billion in the previous fiscal year. The import bill was $64 billion in 2015-16.
"We should increase production and raise our (non-oil) exports and resist America's plots against the sale of our oil," Rouhani said.
The EIA has raised its Brent crude-oil price forecast for 2019 to USD 65 a barrel, up from its earlier projected USD 63 due to the tighter global oil market.
On the Multi Commodity Exchange, crude oil for delivery in May contracts fell by Rs 223, or 4.81 percent, to Rs 4,414 per barrel with a business turnover of 11,120 lots.
Putin said that the deal is effective until the end of June and that he hoped Saudi Arabia will not have to raise its oil production to offset possible exports curbs from Iran due to the US sanctions.
Earlier in the day, Trump had said his efforts to persuade OPEC oil producers to increase output were working and gasoline prices were coming down.
Struggling to meet budget targets, the government had in the just concluded fiscal (2018-19) asked cash-rich PSUs to pay second interim dividend as well as undertake share buyback.
Brent crude futures were at $74.09 per barrel at 0029 GMT, down 26 cents, or 0.4 percent, from their last close.
At the Multi Commodity Exchange, crude oil for May delivery was trading higher by Rs 27, or 0.58 per cent, at Rs 4,656 per barrel in a business turnover of 27,624 lots.
On the Multi Commodity Exchange, crude for delivery in May fell by Rs 19, or 0.41 percent, to trade at Rs 4,622 per barrel in a business turnover of 28,115 lots.
External Affairs Ministry spokesperson Raveesh Kumar said the government will continue to work with partner nations, including with the US, to find all possible ways to protect India's energy and economic security interests.
Spot gold was up 0.4 percent at $1,279.48 per ounce, as of 0325 GMT, having touched $1,270.63 in the previous session - its lowest since Dec. 27, 2018.
Industry sources said Reliance had a contract to buy some 3 million barrels of crude oil from Venezuela a month, which has been reduced to about 2 million barrels already.
International benchmark Brent crude oil futures rose 21 cents, or 0.29 percent, to USD 71.93 a barrel by 0319 GMT. Brent gained as much 0.5 percent to 72.08 a barrel, the highest since November 8 and the highest this year.
At the Multi Commodity Exchange, crude for delivery in April fell by Rs 2, or 0.05 percent, to Rs 4,401 per barrel in a business volume of 18,970 lots.
Brent crude oil futures were at $71.08 a barrel at 0111 GMT, down 10 cents, or 0.1 percent, from their last close. Brent ended down 0.5 percent on Monday.