And the institute says test trials would give the Americans as much as five years warning to develop countermeasures.
The Israelis, who view Iran's nuclear and missile programs as an existential threat, insist Tehran wants to acquire ICBM capability with the U.S. East Coast as its target.
These claims have intensified as Prime Minister Binyamin Netanyahu's right-wing coalition seeks to torpedo U.S.-led Western efforts to negotiate a rapprochement with Iran to scale back its nuclear program.
Israel believes this would rule out any U.S. military action against the Islamic Republic's nuclear project, leaving the Jewish state isolated.
Netanyahu declared on CBS television Oct. 23, shortly after his address to the U.N. General Assembly in New York, that Iran is building ICBMs to reach ... the Americans mainland within a few years."
But the IISS observed in a study released Thursday there's no near-term prospect of that and Iran has two options when it comes to producing ICBMs.
The first is to develop one from an operational intermediate-range missile, or IRBM, like its Sejjil-2 system, a two-stage, solid-fuel missile first test-flown in 2008. It has a range of 1,250 miles.
The second is to expand on liquid-propulsion systems like its Ghadr missile, a single-stage weapon derived from North Korea's No Dong weapon. It has a range of 1,000 miles.
An Iranian ICBM would need a range of 6,250 miles to reach the U.S. East Coast.
The IISS observed France, "whose solid-propellant missile development program matured at a faster pace than Iran's, needed more than decade to advance from a medium-range missile," like Iran's Sejjil-2 with a 14-ton engine, "to a 20-ton motor for the intermediate-range M4 missile.
"It took France another 14 years before it would develop and deploy the 6,250-mile-range M51 missile."
The IISS noted China "experienced a similar timeline" for advancing from medium- to long-range systems with its JL-1/DF-21 and JL-2/DF-31 missiles.
"It is, therefore, reasonable to conclude that Iran is unlikely to move on to producing an operational intermediate-range, powered by a 20- to 25-ton first-stage motor within the next five years.
"An ICBM powered by a first-stage motor in excess of 30 tons would likely require an additional 5- to 10 years, if not more," the study said.
"Under such a timeline, Iran would not be expected to field an operational ICBM before the middle of the next decade," it concluded.
The institute conceded the Iranians "could break with the missile-development experience of other nations ... and forgo development of an IRBM, and proceed directly from Sejjil-2 to an ICBM."
But it said "such a leap in capability would entail considerable technical risk, and would not be consistent with the structured engineering approach Iran has adopted for its missile programs."
There is no "publicly available evidence" it has ground-tested a solid-fuel power plant larger than Sejjil-2's first-stage motor.
"If ground-testing of a 30-ton motor were to start today, an initial flight test could conceivably commence in two- to three years, or late 2015 at the earliest," the study said.
"Based on the experience of others, flight trials ... of the new missiles under operational conditions would require another four years, if not more.
"The soonest Iran might have an operational, solid-propellant ICBM under this scenario would be late 2019," the IISS observed.
"But this assumes that Iran could mature its technical and manufacturing capacity smoothly and efficiently, while skipping the critical step of perfecting an IRBM before attempting to create an ICBM.
"It also assumes that Iran could proceed more quickly than France, China or India did in their respective efforts to develop long-range missiles. There is nothing in Iran's history of missile development to suggest that this is remotely possible."
Iran says it does not seek missiles with a range over 1,250 miles -- enough to blast U.S. warships and air bases in the Persian Gulf or Israel.
Gen. Amir Ali Hajizadeh, commander of the Aerospace Division of the Revolutionary Guards Corps, which oversees Iran's missile program, said Oct. 2 this was "because our enemies are within this range."