Gen. Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, right, confers with his French counterpart, Gen. Pierre de Villiers, aboard the French aircraft carrier Charles de Gaulle in the Persian Gulf on Sunday. (Bob Burns/AP)

When Gen. Martin Dempsey’s plane touched down Sunday on the deck of this ship, he became the first chairman of the Joint Chiefs of Staff in recent history — perhaps ever — to set foot on a French aircraft carrier, a sign of the two nations’ increasing operational unity in the campaign against the Islamic State.

Since the ship arrived in the Persian Gulf last month, U.S. warplanes have landed on the Charles de Gaulle; French and American jets have carried out joint training missions; and the French ship has operated alongside the USS Carl Vinson, another carrier in the same waters. Both ships are now under American command.

The mission marks the first time that France has placed the Charles de Gaulle, the only non-U.S. nuclear aircraft carrier in the world and a jewel of the French military, under the operational command of a foreign nation, a reflection of the importance Paris has placed on combating the ­Islamic State militant group.

The United States continues to shoulder the bulk of the military burden among members of the coalition assembled against the group, which surged out of Syria last year to capture a third of Iraq. Of the 2,738 ­airstrikes the coalition has conducted in Iraq and Syria since last summer, the Americans have carried out 2,203.

Britain, the largest contributor after the United States, had conducted about 160 strikes as of early March. Arab nations, which have launched strikes mainly in Syria rather than in Iraq, have carried out far fewer.

Iraqi forces and Shiite militiamen inch closer to Tikrit as fighting with Islamic State continues. (Reuters)

The picture on the ground in Iraq is similar. Although a growing number of countries have committed soldiers to train and advise Iraqi troops, the U.S. force of just under 3,000 is by far the largest of the coalition. Australia has made the next biggest on-the-ground troop commitment, for a force of about 500, while France has about 120 soldiers. None of the alliance’s Arab members have announced plans to send a training force, according to a coalition spokesman.

The fight against the Islamic State comes as many leaders in Europe confront major fiscal challenges and grapple with questions about what sort of militaries their societies require. In the Middle East, leaders have trod carefully in launching strikes within fellow Arab nations, mindful of precedents they create.

U.S. officials say much of that gap in air power can be explained by superior American military technology, particularly in precision munitions and intelligence collection, and greater U.S. military resources.

Seven months into the air campaign, Dempsey said the contributions of the 20 countries participating in the airstrikes and the three taking part at sea — France, Britain and the United States — have hurt the Islamic State’s capabilities in Iraq.

He and other U.S. officials reject the criticism that the alliance’s use of air power has been too timid. Speaking to reporters aboard the ship, he said coalition aircraft were conducting as many strikes as they reasonably could, given the militants’ efforts to avoid movement in the open, making it more difficult to target them, and the coalition’s desire to prevent civilian casualties.

“We have a responsibility to be very precise in the use of air power,” Dempsey said. “If I had more targets and I could be precise, we could produce more effects on the ground. . . . Carpet-bombing through Iraq is not the answer.”

At the same time, he said he wanted to see more participation in Iraq from neighboring countries.

“If you’re asking me, would I like to see more activities from the coalition, it would generally be on the ground . . . in particular the nations of the region, who have both the greatest to gain and the most to lose, and who also, frankly, can relate to the local populations better than we can,” Dempsey said.

Dempsey visited the Charles de Gaulle along with his French counterpart, Gen. Pierre de ­Villiers, who said the coalition had to balance the desire for quick results with the reality that Iraqi forces need time to prepare for ground offensives. “The Iraqis are the ones who will do this,” he said.

Nevertheless, differences remain in Paris’s and Washington’s approach to the Islamic State, notably France’s decision to forgo airstrikes in Syria. The French government has suggested that such strikes could benefit Syrian President Bashar ­al-Assad, whom Western leaders want to see replaced.

France is flying about 12 to 15 sorties a day from the Charles de Gaulle as part of the campaign against the Islamic State. French planes have dropped munitions in only some of those flights. The remainder are surveillance or air support missions that do not result in strikes. French planes are also flying from Jordan and the United Arab Emirates.

When the French carrier’s gulf operation ends after eight weeks, it will leave the area and head toward India.

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