* Iraq wants 36 sophisticated U.S. combat planes

* Deal delayed months ago when Iraq diverted funds to food

BAGHDAD, Aug 31 (Reuters) - Washington and Baghdad have made significant progress on a deal for Iraq to buy Lockheed Martin F-16 warplanes but do not have a signed contract, a U.S. military official said on Wednesday.

The Iraqi government in February delayed its planned purchase of F-16s and diverted ${esc.dollar}900 million set aside for an initial payment on the aircraft into its national food ration programme to help ease shortages and cool nationwide protests.

But Iraqi Prime Minister Nuri al-Maliki said on July 30 that Iraq would buy 36 F-16s, double the number it had originally planned, to shore up its weak air defences.

The OPEC producer has found itself flush with cash this year, reaping windfall profits as the world oil price has remained above budget projections.

In June Deputy Prime Minister Hussain al-Shahristani said Iraq's oil revenues were ${esc.dollar}8.7 billion, or 34 percent, over projections in the first five months of the year.

"Our two governments are working out the details. They do not have a signed contract yet, but significant progress (has been made) towards it," Major General Jeffrey Buchanan said.

Lockheed Martin, a leading Pentagon supplier and maker of the popular multi-role fighter used by about two dozen countries worldwide, has been involved in the talks, Buchanan said.

The two sides are negotiating on the F-16 Block 52 export model with sophisticated avionics and weapons, Buchanan said.

"If there is in fact a deal it would be the entire standard ... package which includes maintenance, training, training for the maintainers, training for the pilots," he said.

Lockheed Martin said in May it hoped to finalise F-16 sales to Iraq by early next year.

Iraq relies on the U.S. military for air support as it rebuilds its military more than eight years after the invasion that ousted Saddam Hussein. But U.S. forces are scheduled to leave Iraq by year-end under terms of a bilateral security pact.

The two sides are discussing whether to keep some U.S. troops or military trainers in the country next year.

Buchanan said he did not know the value of the possible F-16 contract or whether Iraq intended to buy the 36 combat jets at once or over time. (Reporting by Jim Loney; Editing by Matthew Jones)