After talks in the Saudi capital Riyadh, Nigeria's President Muhammadu Buhari and Saudi King Salman "committed themselves to doing all that is possible to stabilise the market and rebound the oil price," Buhari's office said in a statement.
Buhari was in Riyadh a week after Saudi Arabia, Russia, Venezuela and Qatar agreed at talks in Doha to freeze production at January levels in a bid to stem the dramatic fall in oil prices.
The agreement is conditional on other major producers joining in, as oil heavyweights seek to ensure others do not take advantage of output limits to win market share.
The statement after Tuesday's talks made no mention of Nigeria joining the freeze but analysts say the OPEC member is likely to eventually support the move.
The official Saudi Press Agency also reported that talks between Prince Abdulaziz bin Salman, the Saudi deputy oil minister, and his Nigerian counterpart, junior oil minister Emmanuel Ibe Kachikwu, focused on "the best way for (market) stability" and "the cooperation of producing countries inside and outside OPEC" to achieve this.
Saudi Arabia and its Gulf allies in the Organization of the Petroleum Exporting Countries had been refusing to limit or reduce production, leading to a supply glut that has seen prices fall by 70 percent since mid-2014.
Poorer OPEC members, including Nigeria, have been hard hit by the price drop but even the wealthy Gulf states have been forced to adopt austerity measures to cope with falling oil revenues.
"I wouldn't be surprised to see them voice their support to the freeze agreed in Doha," Abhishek Deshpande, lead oil market analyst at Natixis in London, said of Nigeria.
But he said that unless Iraq and Iran also commit to limit production such talks "carry very little weight".
The two countries are OPEC's second- and third-largest producers.
Iran, returning to world markets as sanctions are lifted under its nuclear deal, has insisted on boosting production to pre-sanctions levels.
"Some neighbouring countries have increased their production over the years to 10 million barrels per day and export this amount, then say let's all freeze our oil production," Oil Minister Bijan Zanganeh said on Tuesday.
"They freeze production at 10 million bpd and we freeze at 1 million bpd. This is a very funny joke."
Saxo Bank analyst Christopher Dembik told AFP that Nigeria's position is "a bit ambiguous," supporting the mooted freeze but at the same time wanting to increase its production to respond to domestic market needs.
Nigeria could be 'crucial'
"In the longer term, there is no reason why the country won't align itself with the position of Saudi Arabia and Russia," Dembik said.
Nigeria and Saudi Arabia would also discuss their position towards Iran and Iraq, he added.
"Nigeria could have a crucial role in this respect because of its measured position" that Iran and Iraq should elevate their production before envisaging freezes, Dembik said.
"It is probable, then, that Nigeria meanwhile establishes a bridge for negotiations, notably between Riyadh and Tehran."
According to OPEC's Monthly Oil Market Report, Iraq produces about 4.4 million barrels a day, followed by Iran at more than 2.9 million.
Saudi Arabia's output is close to 10.1 million barrels a day, according to January data.
Kachikwu, who is head of Nigeria's state-run oil firm, also discussed joint oil and gas investments during his meeting with Abdulaziz, SPA reported.
Oil prices nudged higher Tuesday as the two OPEC members met.
US benchmark West Texas Intermediate crude for delivery in April was up one cent at $33.40 a barrel. Brent North Sea crude for April rose 18 cents to $34.87 compared with Monday's close.
After the Saudi visit, the Nigerian delegation was to travel to Qatar for more oil talks.
