(Corrects to make clear soldier killed in Iraq took second-to-last plot not the last plot)

OVERLAND PARK, Kan., Sept 20 (Reuters) - A Kansas military cemetery has run out of space after two burials in the last week, including that of an Iraq war casualty, officials said on Thursday.

"We are full," said Alison Kohler, spokeswoman for the Fort Riley U.S. Army post, home of the 1st Infantry Division.

U.S. Sens. Sam Brownback and Pat Roberts, both Kansas Republicans, on Thursday sent a letter to William Tuerk, the under secretary for memorial affairs at the Department of Veterans Affairs, urging for full funding for a new cemetery for Fort Riley.

"While a new cemetery would not be completed in time to alleviate this situation immediately, it is vitally important," Roberts and Brownback, a Republican presidential candidate, said in their letter.

"We truly owe our military members a debt of gratitude and the least we can do is provide them with an honorable burial ground," the senators wrote.

Since the 2003 beginning of the war in Iraq, Fort Riley has lost 133 soldiers and airmen, though not all are buried in the Fort Riley cemetery. Sgt Joel Murray, who died Sept. 4 in Iraq, took the second-to-the last available plot, and the final plot was used on Tuesday when an 83-year-old retired veteran was buried, Kohler said.

Fort Riley can bury bodies on top of other bodies if family members want to share a plot, said Kohler.

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