Speaking at the conference, Saudi Oil Minister Khalid al-Falih said market recovery is apparent, and the success of the agreement is obvious, but producers can't relax yet.
"The visit is likely to strengthen trade ties between Russian Federation and Saudi Arabia, but most are wondering whether two of the world's major oil producers will be discussing a collaboration to improve the price of oil", Ahmad said.
US State Department spokesperson Heather Nauert was asked during a recent briefing whether the United States was concerned about the recent moves of its staunch allies - Turkey and Saudi Arabia.
However, the agenda also included issues on which the two sides deeply differ, including the war in Syria.
The Kremlin said ahead of the visit that Salman and Putin will discuss "the situation in the Middle East and North Africa, especially focusing conflict situations in the region".
"This is a landmark event", Mr Putin said in televised comments before the meeting at the Kremlin's opulent St Andrew's Hall.More news: Google just revealed a $49 answer to Amazon's Echo Dot
As Saudi Arabia's King Salman embarked on a historic four-day visit to Russian Federation, the whole world is keenly following the developments.
Oil traded near $50 a barrel in NY as traders weighed a flood of US crude exports against the possibility of extended production cuts by OPEC and Russian Federation.
On Wednesday, Mr Putin said a global deal to cut oil production in order to raise prices could be extended to the end of next year.
Russian Federation is not a member of the oil cartel Opec, but it has collaborated with Opec members on suppressing production to drive up oil prices.
Brent crude was up 70c at $56.50 a barrel by 1.40pm GMT.
Riyadh supports rebels fighting President Bashar al-Assad's forces while Russian troops and Iranian militias have sided with Assad.More news: New Range Rover Sport SVR And Plug-In Hybrid Option Unveiled
Russia's foreign minister, Sergey Lavrov, said after the talks that Mr Putin and King Salman had discussed conflicts in the Middle East, as well as reconfirmed the need to fight terrorism.
His Saudi counterpart, Adel al-Jubeir, said new horizons had opened for Russia-Saudi ties that he could not previously have imagined.
The current talks in Moscow will determine the fate of the package of arms contracts, including the delivery of S-400 Triumf anti-aircraft missile systems to Riyadh. "We seek to strengthen bilateral relations for the sake of peace and security, for the sake of the development of the global economy", the Saudi monarch stressed.
Both Falih and Nasser are part of an official Saudi visit to Moscow.
Plans for a $1 billion joint fund to invest in energy projects are also expected to be finalised.
Another memorandum of understanding was signed under which Russian petrochemicals firm Sibur would explore cooperation with Saudi Arabia.More news: Facebook activates safety check after 50 killed in Las Vegas shooting