The US House of Representatives on Thursday approved a bill that should offer undocumented migrants more protection in the form of legal residency.
The law must prevent so-called 'dreamers', people who came to the US as children without valid residence papers, from being deported.
It must also become easier for them to obtain citizenship.
The proposal was approved by 228 members of the lower house, 197 voted against.
Only nine Republicans agreed to the proposal.
The bill is now being sent to the Senate, where it will likely meet even more resistance from the Republican Party.
US President Joe Biden wants to stop deporting undocumented migrants and actually arrange amnesty, also for the 'dreamers'.
These are hundreds of thousands of people who came to the US as children without valid residence papers and started their adult lives there.
Many of them grew up in the US and received education there.
For a long time they received legal protection, but in 2017 the Donald Trump administration decided to abolish it.
The lower house also approved a second bill to protect about one million migrant workers from deportation.
247 members voted in favor, 174 voted against.
A total of some 2.5 million undocumented migrants must be able to obtain permanent residency within five years through Biden's new policy and American citizenship three years later.
Biden promised to relax legislation
Biden has always opposed the strict migration policies of his predecessor Trump and insisted on the first day of his presidency that he would change the policy.
Legal residency for the undocumented, nearly half of whom are from Mexico, has long been a priority of Democratic and liberal politicians, who believe they contribute to the economy.
It is not known how many people live in the US without valid residency papers, but most estimates put it between 10 and 12 million.
Among them are at least two million people from Central America, mainly El Salvador, Guatemala and Honduras.