WASHINGTON — Pentagon officials have concluded that hundreds more trainers, advisers and commandos from the United States and its allies will need to be sent to Iraq and Syria in the coming months as the campaign to isolate the Islamic State intensifies.

In meetings with President Obama’s national security team in recent weeks, military officials have told the White House that they believe they have made significant progress in the fight against the Islamic State in both Iraq and Syria, administration officials said. But to deal a lasting blow to the extremist Sunni militancy, also known as ISIS and ISIL, they believe that additional forces will be needed to work with Iraqi, Kurdish and Syrian opposition fighters on the ground in the two countries.

In the past, the Pentagon’s requests for additional troops in both Iraq and Afghanistan have been met with skepticism by Mr. Obama, and his aides have said he has resented what he has regarded as efforts to pressure him. But the rise of the Islamic State has alarmed the White House, and a senior administration official said Thursday that the president is willing to consider raising the stakes in both Iraq and Syria.