The 22-nation agency is spearheading one of several efforts to roll back the mass of space junk swirling round the planet from past missions that poses a risk to active satellites.
Aschbacher said 110 countries or entities have joined ESA's Zero Debris charter, which aims to stop any new orbital garbage being generated by 2030.
Asked whether SpaceX, whose satellites now make up some two thirds of spacecraft active in low Earth orbit, had signed up, Aschbacher said: "Not yet, but we are in discussion with them... This is a charter that keeps evolving and... we will keep raising the topics because they are so fundamental."
SpaceX did not immediately respond to a request for comment.
Of the roughly 10,300 active satellites in orbit, roughly 6,300 are part of SpaceX's fast-growing Starlink constellation, according to the U.S. Space Force.
China has begun to launch constellations of its own to compete with Starlink, as has Amazon, which expects to launch over 3,000 satellites for its Kuiper constellation this decade.
Amazon has signed up to the charter, Aschbacher said.
There are currently 18,897 pieces of trackable space junk in orbit, according to Jonathan McDowell, a Harvard astronomer who tracks such objects.
Space debris and junk are often used interchangeably, but some consider space junk to include inactive payloads and rocket bodies as well as debris, or errant shards of broken satellites.
There are no international laws on debris, but countries and space agencies have begun in recent years to devise proposals and national rules for tackling the problem.
"We are not a regulatory body; we are a technical space agency," Aschbacher said.
"But the fact that we have put the charter around the table, which was elaborated with all the other partners, and that they signed up to it is very encouraging."
MISSILE TESTS
SpaceX is subject to orbital debris requirements from the U.S. Federal Communications Commission.
A Starlink satellite is required to deorbit - or burn up in Earth's atmosphere - within five years of the end of its life.
"I think it's very important to have industry publicly commit to this sort of initiative, so I'm glad to know SpaceX is considering it," McDowell said, referring to the charter.
In 2023, SpaceX criticised a Federal Aviation Administration report warning of the risk to people from falling debris from constellations as "deeply flawed", SpaceNews reported.
Although commercial constellations dominate the spotlight, much of the growing tide of space junk is seen as driven by collisions or reports of anti-satellite missile tests.
A Chinese rocket body in August broke apart in an apparent collision with a piece of space junk, creating one of the largest fields of debris in recent history.
According to NASA, two earlier incidents increased the junk pile by around 70%. These were the destruction of the Chinese Fengyun-1C spacecraft in 2007, which the United States said at the time was caused by a Chinese missile, and the accidental collision of a U.S. and Russian spacecraft in 2009.
In 2021, a Russian anti-satellite missile test added at least 1,500 pieces of debris, some of which have decayed since, U.S. Space Command said at the time.
The U.S. in 2008 and India in 2019 both demonstrated anti-satellite missiles that added to the debris field.
The Biden administration has promoted a moratorium on such tests, with several countries signing on but not Russia or China.
