ARBIL, Iraq (Reuters) - Iraq's Kurdish region has sent reinforcements to a disputed area where its troops are involved in a standoff with the Iraqi army, a senior Kurdish military official said, despite calls on both sides for dialogue to calm the situation.

The second military buildup this year illustrates how far relations between Baghdad's central government, led by Shi'ite Muslim Arabs, and ethnic Kurds have deteriorated, testing Iraq's federal cohesion nearly a year after U.S. troops left.

Baghdad and Iraq's autonomous Kurdistan region earlier this week began sending troops to an area over which they both claim jurisdiction, raising tensions in a long-running feud over land and oil rights.

More Kurdish troops and tanks were mobilised on Saturday and headed towards the disputed areas, the deputy minister for Kurdish military affairs said late on Saturday, adding that they would hold their positions unless Iraqi forces made a move.

"If they overstep the line, we will strike them," Anwar Haji Osman said.

The Iraqi army and Kurdish troops have previously come close to confrontation only to pull back at the last moment, flexing their muscles but lacking any real appetite for a fight.

Iraq's speaker of parliament, who visited Kurdish President Massoud Barzani on Friday, said "significant progress" had been made towards defusing the standoff and that a meeting between military leaders from both sides would be held on Monday in the Defence Ministry in Baghdad.

Washington intervened to end a similar standoff in August and is again in contact with Iraqi and Kurdish officials to ease tension mounting over the formation of a new command center for Iraqi forces to operate in the disputed areas.

Kurds say the Dijla Operations Command is a threat to them and an attempt by Prime Minister Nuri al-Maliki to seize control over the oil rich territories along the internal border that demarcates the Kurdish region from the rest of Iraq.

Maliki says the Dijla Operations Command is necessary to keep order in one of the most volatile parts of the country.

Barzani on Saturday turned down an invitation from Shi'ite cleric and lawmaker Moqtada al-Sadr to meet with Maliki to discuss the situation.

In a statement posted on the Kurdistan regional government's website, Barzani's spokesman said he had refused because the matter was not personal, but rather a result of Maliki's "constant non-commitment to the constitution".

The latest flare-up began one week ago when Iraqi troops went after a fuel smuggler who had taken refuge in the office of a Kurdish political party in Tuz Khurmato, 170 km (106 miles) north of the capital, sparking a clash with Kurdish Peshmerga fighters in which one passerby was killed.

Maliki has sparred more aggressively with Barzani since the withdrawal last year of U.S. troops who had served as a buffer between the federal Baghdad government and Kurdistan.

(Writing by Isabel Coles; Editing by Paul Simao)