Saudi Arabia has announced the formation of an “Islamic military alliance” to combat global terrorism, an effort to respond to Western assertions that it could do more in the fight against the Islamic State and to solidify its claim to leadership of the Sunni world against Shiite Iran.

The 34-member group, to be headquartered in Riyadh, will coordinate mutual anti-terrorism assistance for members “all over the Islamic world,” Deputy Crown Prince and Defense Minister Mohammed bin Salman said in a rare news conference Tuesday.

“Today, every Islamic country is fighting terrorism individually,” Prince Mohammed said in remarks reported by the official Saudi News Agency. The new alliance, he said, “emanates from the keenness of the Muslim world to fight this disease, which affected the Islamic world first, before the international community as a whole.”

Saudi Foreign Minister Adel al-Jubeir, speaking at a news conference in Paris, said that “in terms of the operation of this coalition . . . nothing is off the table. It depends on the requests that come, depends on the need, and it depends on the willingness of countries to provide the support that is necessary.”

In addition to a military component, he said it would include “stopping the flow of funds” to terrorists and “confronting the ideology of extremism that promotes killing of the innocent, which is contrary to every religion, particularly the Islamic faith.”

The Obama administration has called repeatedly on all partners in the anti-terrorism fight to increase their efforts. “Yes, we’d like the [Persian] Gulf countries to do more,” Defense Secretary Ashton B. Carter said during a visit to the Middle East on Tuesday. He said he had made suggestions to “all the coalition partners . . .­ about things that I thought that they could contribute.”

The administration said it welcomed the new alliance. Both Washington and Riyadh emphasized that it was not intended to supersede or interfere with U.S.-led military operations against the Islamic State — also known as ISIL and ISIS — in Syria and Iraq. Prince Mohammed said his government’s activities in those countries would only be carried out in coordination with the “international community.”

“I think the Saudis went to great lengths to also make it clear that this is not a substitute or a replacement for the 65-member anti-ISIL coalition that was built and is being led by the United States of America,” White House press secretary Josh Earnest said.

Earnest said that in addition to other activities, the new alliance would focus on “countering ISIL’s online radicalization efforts.”

Turkey, one of the members of the new alliance, drew a direct line between the need for the alliance and growing criticism of Islam in the West. “The raising of Muslim countries’ voices together against terror is the best response to those who try to associate terror with Islam,” Turkish Prime Minister Ahmet Davutoglu said at a news conference in Ankara. “We consider this effort by Muslim countries as a step taken in the right direction.”

Pakistani Foreign Secretary Aizaz Chaudhry told reporters in Islamabad that he was surprised to see news of Pakistan’s inclusion on the list. He said he had asked for clarification from the country’s ambassador in Riyadh, Pakistani media reported.

Senior administration officials, speaking on the condition of anonymity about government-to-government conversations, said they also expected some Arab states to announce in the near future that they will resume air and other military operations against the Islamic State in Syria.

Saudi Arabia, the United Arab Emirates and Jordan have flown virtually no strike missions there since early summer.

In the case of the Saudis and Emirates, resources have been diverted to Yemen, where they are combating what they say are Iran-backed local fighters who seized power earlier this year.

Saudi Arabia has been keen to assume the role of regional leader at the head of Sunni-dominated countries, particularly in the face of what it sees as Iran’s bid for regional hegemony, which it believes will increase in the wake of the Iran nuclear deal.

The Saudis did not release a membership list, but the alliance includes powerful military players such as Egypt and Pakistan, in addition to Turkey. The Associated Press reported from Riyadh that the UAE, Bahrain, Qatar, Kuwait, Lebanon, Libya, Jordan, Tunisia, Yemen, the Palestinians, Morocco, Bangladesh, Malaysia, Benin, Chad, Togo, Djibouti, Senegal, Sudan, Sierra Leone, Somalia, Gabon, Guinea, Comoros, Ivory Coast, Maldives, Mali, Mauritania, Niger and Nigeria are members.

All have had problems in varying degrees with extremism and terrorism, including but not limited to the Islamic State. Although some of the African members do not have Muslim majorities, all have sizable Sunni populations.

Jubeir said the sectarian divide was not a factor in the new organization. “This is not a Sunni coalition or a Shia coalition,” he said. “It is an anti-terror coalition, it is an anti-extremist coalition” whose activities will not be limited to countering the Islamic State.

The list does not include Iraq, which is closely allied with Iran.

Jubeir was indirectly critical of U.S.-led anti-terrorism campaigns, saying that “the efforts to go after terrorism and extremism so far have been, while noble and commendable, have not been, we believe, as effective as they could have been if there had been a global effort to do so.”

It was not entirely clear what tasks the new alliance would undertake, and where. Jubeir said that “the objective here is to bring together the military and security experts so that they can work out the modalities of how we move forward.”

“I can’t tell you we have a list of things we want to go to,” he said, but “if countries need help, they can come and request that assistance, and countries­ . . . can provide that assistance on the spot” on a “case by case basis.”

Jubeir said each government would have to make its own decision about requesting, or offering, assistance — including “military training or equipment or . . . technical assistance in terms of messaging . . . to counter the ideology of violent extremism.”

“I believe there are a number of countries that are in desperate need of assistance, all types of assistance,” he said, “and I believe there are a sufficient number of countries that are ready to provide such assistance.”