By Kristin Roberts

QUEBEC CITY, April 11 (Reuters) - NATO allies with forces in Afghanistan's volatile southern region will meet on Thursday to grapple with lingering shortfalls in troops and equipment as casualties mount amid spring fighting with the Taliban.

U.S. Defense Secretary Robert Gates will press the group to scour their inventories for supplies that can be sent to the war zone. But he will not offer any more troops or equipment, according to a senior defense official traveling with the secretary.

"We are not expecting to put down any additional offers on the table," the official said ahead of Gates' arrival in Canada on Wednesday evening.

The meeting of defense ministers in Quebec City begins a day after the bodies of six Canadian soldiers killed in a roadside bomb attack in Afghanistan were to return home. Those deaths on Sunday brought the Canadian toll in the war to 51, the highest of all coalition countries except the United States and Britain.

NATO has 35,000 troops in Afghanistan, with most forces engaged in the south and east where the Taliban has regrouped.

NATO commanders have for months requested additional troops and equipment, and U.S. and British officials have expressed frustration about the unwillingness of some allies to contribute.

Most of the NATO force, or 23,000 troops, are either American or British. Australia this week said it would double its troops in Afghanistan. The Netherlands, Denmark, Romania and Estonia also have forces in Afghanistan's south.

Despite the call from commanders, some allies, such as France and Italy, have declined to increase their force levels, citing commitments elsewhere. Some also have imposed restrictions, known as caveats, on how their troops can be used in the war zone.

NATO still needs additional maneuver forces and aircraft, according to U.S. and NATO officials. A NATO official has said alliance commanders need the equivalent of a battalion of soldiers. A battalion totals about 500 to 1,000 soldiers.

The senior U.S. defense official said those shortfalls would not likely be filled during Thursday's meetings.

"I don't think there's an expectation that we can fill them at this meeting," the official said.

But Gates will urge the group to identify equipment they can contribute and identify other NATO allies that could be pressured to help more.

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