* First Maliki visit to Kurds in more than two years
* Little expectation of breakthrough in talks
* Shi'ite premier facing Sunni protests, surge in violence (Adds comments from Maliki and Barzani)
By Isabel Coles and Suadad al-Salhy
ARBIL/BAGHDAD, Iraq, June 9 (Reuters) - Iraqi Prime Minister Nuri al-Maliki visited the Kurdistan region on Sunday for the first time in more than two years, in a symbolic step towards resolving a long-running dispute over oil and land that has strained Iraq's unity to the limit.
Better relations with the Kurds could take some pressure off the country's Shi'ite leadership, which is facing a surge of violence it blames on Sunni Islamist insurgents invigorated by the civil war in neighbouring Syria.
The Shi'ite premier was met on the tarmac at Arbil airport by Kurdistan President Masoud Barzani, who smiled and shook hands with a man he has previously likened to a dictator.
Maliki's last official trip to Kurdistan was in 2010, when the "Arbil Agreement" was struck, allowing him to form a power-sharing government among majority Shi'ite Muslims, Sunnis and ethnic Kurds after months of wrangling.
That deal, like others thereafter, was never fully implemented, and the central government in Baghdad and the autonomous Kurdish region have since been at odds over oil and disputed territories along their internal boundary.
Sunday's rare visit produced little of substance on those issues, but both sides said there was now a positive atmosphere in which to hold more talks.
"Neither I nor President Barzani have a magic wand," said Maliki at a joint news conference following a cabinet session and a one-on-one meeting between the two leaders. "The important thing is our shared desire to reach solutions."
Barzani warned last week that, unless the current talks succeed, the self-ruled region would be forced to seek a "new form of relations" with Baghdad.
Kurdistan has been an autonomous part of Iraq since 1991, running its own administration and armed forces, but it relies on the national government for a share of the budget financed by the OPEC nation's oil revenues.
In recent years, the Kurds have signed contracts on their own terms with the likes of Exxon Mobil, Total and Chevron Corp, antagonising Baghdad, which insists it alone is entitled to control exploration of Iraq's oil.
Kurdistan used to ship crude through a pipeline network controlled by Baghdad, but exports via that channel stopped last December due to a row over payments for oil companies operating in the northern enclave.
The region says the constitution allows it to exploit the reserves under its soil, and is building the final stretch of an independent oil export pipeline that could help it to break its reliance on a share of the federal budget.
The United States opposes that project for fear it would precipitate the break-up of Iraq.
In a statement, the U.S. embassy in Baghdad welcomed Sunday's meeting as "another sign that Iraqi leaders are committed to strengthening their state under the Iraqi Constitution and isolating the terrorists and criminal groups who seek to sow sectarian strife".
Land is another major sticking point between Baghdad and the Kurds. The Iraqi army and Kurdish "peshmerga" troops last year deployed to an oil-rich band of territory over which both claim jurisdiction.
Easing relations with the Kurds would help Maliki, who is facing an intensified campaign by Sunni Islamist insurgents and months of protests by Sunni leaders who accuse the Shi'ite premier of marginalising them.
"Maliki concedes when he feels vulnerable, not when he's strong. The Kurds have recognised for some time now there has been an emerging opportunity to get Maliki to cooperate," said Ramzy Mardini at the Beirut-based Iraq Institute for Strategic Studies.
"Since the local and regional threat is coming from the Sunni side, the Kurds can move in and try to extract concessions from Maliki in exchange for cooperation."
A suicide bomber killed at least seven people at a checkpoint outside a Shi'ite district in Baghdad on Sunday. (Editing by Patrick Markey and Tom Pfeiffer)