WASHINGTON — The Trump administration has decided that it needs no new legal authority from Congress to indefinitely keep American military forces deployed in Syria and Iraq, even in territory that has been cleared of Islamic State fighters, according to Pentagon and State Department officials.

In a pair of letters, the officials illuminated the Trump administration’s planning for an open-ended mission of forces in Syria beyond the Islamic State fight. Secretary of State Rex W. Tillerson foreshadowed the plan in a speech last month, saying that troops will stay in Syria to curb Iran and prevent the Syrian government from reconquering rebel-held areas.

Though Mr. Tillerson also cited a need to mop up the remnants of the Islamic State and keep from leaving a vacuum in which the group could regenerate, other administration officials put far greater emphasis on the extremists. In the letters, they said that the continued potential threat from the Islamic State provided a legal rationale for the Trump administration to keep American troops deployed there indefinitely.

“Just as when we previously removed U.S. forces prematurely, the group will look to exploit any abatement in pressure to regenerate capabilities and reestablish local control of territory,” wrote David Trachtenberg, the deputy undersecretary of defense for policy.