At the rally, organized by the Illinois-based Republican Hindu Coalition, they urged President Trump to cut through the backlog and place a higher priority on the problems faced by immigrants in the United States legally.
"When I came here, my daughter was 6 years old," said Nandu Konduri, 45, a software engineer in North Carolina who has been waiting for his green card application to be processed since 2007. "Many kids have already aged out. We feel stuck."
Indians are among the country's fastest-growing immigrant populations, with about 3.5 million people nationwide and nearly 137,000 Indian immigrants in the Washington region, according to U.S. Census estimates.
With Trump also believed to be considering reforms that would prevent H1-B holders from extending their three-year visas, some anxiety has rippled through that community as well as others with large numbers of high-skilled workers in the country.
Some groups have found hope in a Trump proposal, announced last month, that calls for assigning points to green card applicants based on such factors as age, education and English skills. Under that plan, family-based immigration — in which U.S. citizens and legal permanent residents can sponsor their family members — would be limited to spouses and minor children.
Trump's plan also offers a path to citizenship for millions of undocumented immigrants brought into the country as children in exchange for those reforms and $25 billion in funding for a wall on the U.S.-Mexico border — a deal Democrats in Congress have said would be dead on arrival.
On Saturday, the demonstrators tried to whip up support for the Trump proposal, marching up Pennsylvania Avenue while chanting "Indians love Trump" and "Clear green card backlog."
One message was a play on the Deferred Action for Childhood Arrivals program — benefiting 690,000 people — that Trump has ordered canceled, also known as DACA.
The demonstrators referred to their children as the "DALCA" group, an acronym for a lamb curry dish that, in this instance, also reminded bystanders that the "L" stands for "legal" immigrants.
"No DACA without DALCA" the demonstrators chanted.
Organizers with the Republican Hindu Coalition say the message isn't rooted in resentment.
"We're simply saying: 'Please, deal with us in the same way that you are helping them,' " said Krishna Mullakuri, 31, a software engineer in Virginia who has waited six years for his green card application to be processed.
"Our children also did not choose to come here. We are also trying to give them a better life here."
The organization is calling for children of high-skilled workers awaiting green cards to be granted legal permanent residency immediately. The DACA group should be forced to pay a $25,000 fine over 10 years to stay, it says.
Ramesh Ramanathan, a software engineer in Gainesville, Va., who applied for his green card in 2011, said he worries that his 13-year-old daughter, Akshita, will suffer academically if she's not granted a green card.
After arriving from India as a toddler, Akshita is considering a career as a doctor. Her father knows that goal would be harder to obtain if she's still a foreign national.
"Time is passing by quickly," Ramanathan said. "She has dreams — big dreams."