In the open letter, the Labour MPs said "this government will only succeed if it is able to get a grip on illegal migration".
A key part of this, the letter said, "must be tackling illegal off-the-books employment, which is a major draw for migrants entering our country unlawfully".
"Digital ID would help counter these practices," the MPs said.
Richards - the MP for Rother Valley - said the system for managing and tracking people who enter the country illegally was "fraught with inefficiencies".
He added: "Digital processing and some form of digital ID for those that arrive would help us control the system much more effectively."
The letter also said digital ID could "transform public services" by making it easier to access the NHS, tailoring education and cracking down on benefits fraud.
But the letter said any digital ID programme "must be developed with care, respecting an individual's privacy".
The letter was signed by MPs from the Labour Growth Group, the Red Wall Group representing seats in the Midlands and north of England, and the socially conservative Blue Labour group. Many of them were elected for the first time last year.
Polling by YouGov suggests there is strong support for the introduction of a system of national identity cards in the UK.
Bur critics of such forms of ID have raised concerns about privacy, civil liberties and the collection of data by the state.
An online wallet already allows users to store government-issued documents on their phones, and a digital driving licence is being launched this year.
A government spokesperson said: "We are committed to using technology to improve lives and transform public services.
"Digital identities offer a secure, efficient way for people to prove who they are without physical documents, reducing fraud and saving time.
"Trusted providers following government rules are already conducting hundreds of thousands of digital checks monthly, helping people access employment, housing, and vital services more quickly and easily, while boosting productivity, driving economic efficiency, and supporting long-term growth as part of our plan for change."