* Sadr joins call for Maliki to withdraw bid for third term
* Embattled PM refusing to yield to critics
* Iraqi army fighting militants near rebel-held Tikrit
* Iraqi security 'analysing video' purporting to be Baghdadi (Adds government reports of fighting near Tikrit, comment on Baghdadi video)
By Raheem Salman
BAGHDAD, July 6 (Reuters) - Iraqi Prime Minister Nuri al-Maliki's coalition should withdraw its support for his bid for a third term and pick another candidate, Shi'ite Muslim cleric Moqtada al-Sadr urged, amid parliamentary deadlock over the formation of a new government.
Maliki has come under mounting pressure since Islamic State militants took swathes of the north and west of Iraq last month and declared a caliphate on land they and other Sunni armed groups have captured in Iraq and Syria.
In a statement published on his website late on Saturday, Sadr said Maliki "has involved himself and us in long security quarrels and big political crises" and suggested that preventing Maliki from serving a third term would be a "welcome step".
"It is necessary to demonstrate the national and paternal spirit by aiming for a higher, wider goal from individuals and blocs and by that I mean changing the candidates," said Sadr, who gained political influence during the U.S. occupation.
The radical cleric and his political allies had previously advocated the next prime minister should be a Shi'ite chosen from outside of Maliki's State of Law coalition.
"I remain convinced that the brothers in the State of Law coalition must present the candidate for prime minister ... because it is the biggest bloc within the National Alliance," Sadr said.
State of Law is part of the National Alliance, a bloc comprising the country's biggest Shi'ite parties, including both Maliki's list and his foes.
Dhiya al-Asadi, secretary general of the Al-Ahrar bloc, the Shi'ite political party loyal to Sadr, told Reuters: "We are fine with any State of Law candidate as long as he is not Maliki."
The United States, Iran, the United Nations and Iraq's own Shi'ite clerics have called on Iraqi politicians to overcome their differences to face the insurgency.
Maliki's military spokesman Qassim Atta told reporters on Sunday "the security apparatus is working" to analyse a video posted online of a man purporting to be the leader of Islamic State praying at the grand mosque in Mosul.
The city is one of those seized by the Islamic State in Iraq and the Levant (ISIL) last month before the group changed its name and declared its leader Abu Bakr al-Baghdadi caliph, a title held by successors of the Prophet Mohammad.
Interior Ministry spokesman Saad Maan had earlier said the 21-minute video, which carried Friday's date, was "false".
Atta said the video was being "cross-referenced with intelligence data to determine whether it is in fact" the reclusive Baghdadi.
Before the video was released on jihadist forums and Twitter accounts associated with the group, reports appeared on social media that Baghdadi would make his first public appearance.
Government forces were on Sunday continuing to battle Islamic State militants south of the rebel-held city of Tikrit, which the army has yet to retake after an offensive began on June 28, Atta said.
He said forces had killed 14 militants since Saturday in the al-Dayoum and Wadi Shisheen areas near Tikrit and troops were reinforcing the village of Awja, recaptured three days ago, and preparing to push 8 km (5 miles) north into the city.
Maliki's opponents blame his divisive rule for fuelling the political crisis and want him to step aside. They accuse him of ruling for the Shi'ite majority at the expense of the Sunni and Kurdish minorities.
He has remained defiant, insisting on Friday that he will not give up his quest for a third term in power.
The first meeting of the Iraqi parliament since its election in April collapsed last week without agreement. Kurds and Sunnis walked out, complaining Shi'ite lawmakers had not yet determined who they would put forward as premier.
Maliki's main Shi'ite rivals say there is consensus among some in the Shi'ite coalition and among the Sunnis and Kurds against his bid for a third term.
"There is a wish by all political blocs except the State of Law ... (for) the change," said Ali Shubber, a leading member of the Islamic Supreme Council of Iraq (ISCI), a Shi'ite party that came second to Maliki's State of Law in April's election.
"We feel that it must take place in order to change the political equation."
Another Shi'ite politician, former prime minister Iyad Allawi, called on Maliki on Saturday to give up his bid for a third term or risk the dismemberment of Iraq.
(Additional reporting by Ned Parker and Maggie Fick; Writing by Maggie Fick; Editing by Janet Lawrence)