The resolution's fate is less clear in the US Senate, which is controlled by Trump's fellow Republicans, though some Republicans have expressed concern about his declaration.
In a separate letter on Monday, 23 former Republican US lawmakers also urged current members of Congress to pass the resolution, Politico reported.
Even if it passes, Trump has said he would veto it, and Congress would need to muster two-thirds of lawmakers to override a veto.
Trump on Monday continued to defend the declaration on Twitter and called on Republican senators to stand by him. "Be strong and smart, don't fall into the Democrats 'trap' of Open Borders and Crime!" he wrote.
The former security officials, in Monday's letter, cited US government statistics showing illegal border crossings at nearly 40-year lows. They also pointed to other government data on drug trafficking that showed most opioids enter the country via legal entry points -- something they said a border wall would not stop.
While the letter included both Republicans and Democrats, as well as career civil servants who served under presidents of both parties, the bulk of its most senior signatories rose to their top positions under Democratic presidents.
Among these former officials were CIA Director and Defense Secretary Leon Panetta, CIA Director John Brennan, White House National Security Adviser Susan Rice, Deputy Secretary of State Antony Blinken and Deputy CIA Director David Cohen, all of whom held those posts under Democratic President Barack Obama.
However, the list also included lower-level former officials such as John Bellinger, a former State Department legal adviser, and Eliot Cohen, a former State Department counsellor, both of whom served under Republican President George W Bush.
Democratic Speaker of the House, Nancy Pelosi said, 'To defend our democracy the House will pass Congressman Castro's privileged resolution to terminate the emergency declaration tomorrow.'