This appears to be part of an effort by Maliki, who has moved closer to eastern neighbor Iran since U.S. forces withdrew from Iraq in December 2011, to back off the relationship with the United States in favor of Russia.
Under Vladimir Putin, restored as president, Russia's been driving to restore its Cold War influence in the Arab world.
Maliki signed a $4.2 billion arms deal with Russia Oct. 9 during a high-profile three-day visit. That makes Iraq Russia's second largest defense client after India.
Maliki, accompanied by a posse of Cabinet ministers, also discussed energy cooperation and possible oil contracts with Putin and his advisers.
Few details of those discussions have been released. But they could signal an opening up by Iraq to Russian oil and gas companies that have not fared too well since Maliki's government began parceling out 20-year production contracts to foreign oil companies in 2009.
Maliki's current inclination toward Russia, and China too for that matter, has rung alarm bells in Washington, which has seen its influence in the Iraq and the rest of the Arab world undercut over the last decade, while Iran's standing in Iraq has steadily grown, despite their historical enmity.
Maliki spent 20 years in exile in Iran during the 1980s and 90s hunted by Saddam Hussein's security services for fighting the Baathist regime in Baghdad.
In Saddam's day, Moscow was Iraq's main arms supplier, and lost defense contracts worth some $8 billion after he was toppled in the U.S. invasion of 2003.
"Maliki still remains an enigma in Washington," observed veteran analyst M.K. Bhadrakumar, a former Indian ambassador to a string of regional states.
"He is no doubt a friend of the United States, but he's also possibly more than a friend of Iran. Now, it seems, he is also fond of Russia -- as Saddam Hussein used to be...
"Maliki can be expected to boot out Big Oil ... from Iraq's oil sector. The implications are profound for the world oil market since Iraq's fabulous oil reserves match Saudi Arabia's," Bhadrakumar noted.
Maliki has been gunning for Exxon Mobil, the world's largest oil company, since October 2011 when it signed an extensive exploration deal with the Kurdistan Regional Government, which runs the semiautonomous enclave in northern Iraq which has long had ambitions of independence.
Kurdistan sits on an estimated 45 billion barrels of oil, part of Iraq's state reserves of 431 billion, and the Kurds clearly envision that as the economic core of an independent state.
Baghdad insists only the central government has the authority to sign energy deals, but this has not stopped other international oil majors, such as Chevron and Total of France from signing similar deals with the KRG.
Baghdad fears such renegade agreements encourage secessionist aspirations in Kurdistan, as well as other regions which seek greater autonomy from a regime at a time when Maliki's widely accused of seeking to amass dictatorial powers.
Turkey, Iraq's northern neighbor with ambitions of becoming the regional oil hub between East and West, has also been courting the land-locked Kurds, offering to build an oil pipeline to its Mediterranean terminal at Ceyhan to give them an export route outside Baghdad's control.
"Washington and Ankara have annoyed Maliki repeatedly, taking him for granted, even writing off his political future, by consorting with Kurdistan over lucrative oil deals, ignoring his protests that Iraq is a sovereign state ... and has a constitution under which foreign countries should not have direct dealings with its regions, bypassing the central government," Bhadrakumar wrote in Asia Times Online.
"Kurdistan is already a de facto independent region, thanks to U.S. and Turkish interference.
"The Russia visit shows that Maliki is signaling he has had enough and won't take this affront to Iraq sovereignty anymore ... The plain truth is the 'Russians are coming' and this time they are capitalists and globalists," Bhadrakumar wrote.
The Russians have already gained a foothold in Iraq's energy industry and infrastructure projects.
But, some sources say, the deals that may now be in the works could well dwarf the arms deal Maliki signed in Moscow.