Inside Syria, the administration is prepared to add dozens of Special Operations forces to the 50 who now advise and assist Syrian rebels fighting the Islamic State, say three Defense Department and military officials. The additional trainers, who could total as many as 200, would be able to expand their instruction to Syrian Arab fighters, who are likely to play a pivotal role in capturing Raqqa, the Islamic State’s de facto capital in Syria, the officials said.

The administration’s plans for Iraq are more complicated.

Pentagon officials would like to increase efforts to advise and train Iraqi security forces for the anticipated assault on Mosul, Iraq’s second largest city and the Islamic State’s main stronghold in the country. The plan calls for shifting trainers who are already in the country to positions closer to Mosul, the officials said. They would also like to deploy Apache helicopter gunships — which are already in Iraq, but used only to protect American personnel — and order them to participate in the battle for Mosul.

But the government of Iraq’s prime minister, Haider al-Abadi, has been battling internal political turmoil. His challenges include political opponents, rampant corruption and an economy weakened by low oil prices.