House Speaker Nancy Pelosi said a vote on the measure would come on Tuesday.
The move starts the clock on a constitutional clash between Trump and Democrats and sets up a vote by the full House as soon as next week.
Senate Democratic leader Chuck Schumer also plans to introduce such a resolution. The measure needs only a simple majority in both chambers. It will need the votes of at least four Republicans to pass the Senate, assuming all the Democrats and the two independents there back it.
The Democratic-controlled House is sure to pass the measure, and the Republican-run Senate may adopt it as well despite Trump’s opposition.
If both chambers pass the resolution it would then go to Trump, who said he would veto the resolution.
“On the wall? Will I veto it? One hundred percent. One hundred percent, and I don’t think it survives a veto. We have too many smart people that want border security, so I can’t imagine that it could survive a veto,” Trump told reporters in the Oval Office on Friday.
A Trump veto would likely be sustained, but the upcoming battle will test Republican support for Trump’s move, which some of his allies view as a stretch – and a slap at Congress’s control over the power of the federal purse.
“What the president is attempting is an unconstitutional power grab,” said Democratic Representative Joaquin Castro, the sponsor of the resolution, on a call with reporters.
“There is no emergency at the border,” he added.
Pelosi added that the measure would “reassert our system of checks and balances”.
The battle is over an emergency declaration Trump issued to access billions of dollars beyond what Congress has authorised to start erecting border barriers. Building his proposed wall was the most visible trademark of Trump’s presidential campaign.
Congress last week approved a vast spending bill providing nearly $1.4bn to build 55 miles (89km) of border barriers in Texas’s Rio Grande Valley while preventing a renewed government shutdown. That measure represented a rejection of Trump’s demand for $5.7bn to construct more than 200 miles (322km).
Trump signed the bill, but also declared a national emergency and used other authorities that he says give him access to an additional $6.6bn. That money would be transferred from a federal asset forfeiture fund, Defense Department anti-drug efforts and a military construction fund. Federal officials have yet to identify which projects would be affected.
Castro said he has already garnered support from a majority of the Democratic-controlled House as co-sponsors and that he has at least one Republican sponsor, Justin Amash of Michigan.
Castro’s measure says Trump’s emergency declaration “is hereby terminated”. Castro chairs the 38-member Congressional Hispanic Caucus.
Pelosi wrote that the Republican president’s “decision to go outside the bounds of the law to try to get what he failed to achieve in the constitutional legislative process violates the Constitution and must be terminated”.
A coalition of 16 US states led by California also sued Trump and top members of his administration on Monday to block his decision to declare the emergency.
The lawsuit said Trump’s declaration was a misuse of presidential power.