At the time, Roy explained if he did not object, "Congress will have passed into law a bill that spends $19 billion of taxpayer money without members of Congress being present in our nation's capital to vote on it".
When the House returns from a week-long Memorial Day recess it is expected to bring the legislation back to the House floor for likely passage.
The Senate was able to pass the bill by an 85-8 vote before its members left Thursday evening.
The conservative Republican single-handedly blocked approval of a $19.1 billion relief bill Friday for regions around the USA recovering from hurricanes and other disasters.
The full House is not due back in Washington until June 3.
Under House rules, it only took one opposing member to derail the vote.
"House Republicans' last-minute sabotage of an overwhelmingly bipartisan disaster relief bill is an act of staggering political cynicism", Pelosi said.
Rep. Roy, a member of the House Freedom Caucus, objected to a unanimous consent vote, which would allow the bill to pass without having every congressman vote on the bill itself.
"It is a bill that that includes nothing to address the global emergency and humanitarian crisis we face at our southern border", Roy said. He told his congressional colleagues that the US needed to "have a responsive and fiscally responsive approach to help people who are hurting in the wake of natural disasters" but that he did not want "to let the swamp continue to mortgage the future of our children and grandchildren".
Railing against the "swamp", Roy objected to speeding the measure through a nearly-empty chamber, complained it wasn't paid for and challenged a decision not to include President Trump's $4.5 billion request for dealing with the migrant crisis on the U.S. -Mexico border. "We should have had a vigorous debate and we should have a debate about why we're not securing the border and why we're spending money we don't have", he added.
Senator Lindsey Graham has shown great loyalty to President Donald Trump over the past two years or so, particularly in what critics see as a shameless and diametric rhetorical difference from what the SC senator said of then-candidate Trump during the GOP primaries.
Disagreements on how much funding to give Puerto Rico - which is still recovering from Hurricane Maria - have already delayed the bill.
The border money was just one of the hiccups in the disaster bill.
She later tweeted it was "irresponsible that Republicans would object and make these Americans wait longer to receive the help they desperately need".
House Speaker Nancy Pelosi denounced the action as an example of Republican obstructionism.
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