Texas Senator John Cornyn has played a key role in drafting the framework of a proposed firearms bill following mass shootings in Texas and New York.
Leaving Washington, he said: “I’m through talking.”
The plans include tougher checks for buyers under the age of 21 and cracking down on illegal gun purchases.
The proposals have shown some rare cross-party cooperation on the issue of gun control, but still fall far short of what many Democrats and activists have been calling for.
Recent attempts to tighten gun laws in the US – which has the highest rate of firearms deaths among the world’s wealthy nations – have failed to get the required support in Congress.
The flurry of action comes after 19 young children and two adults were killed at a school in Uvalde, Texas, less than two weeks after a racially motivated shooting at a grocery store in Buffalo, New York, left 10 dead.
But Mr Cornyn’s walk-out has placed a question mark over the legislation’s future. Axios, a political outlet, reported earlier on Thursday that conservative colleagues of the Texas senator are frustrated at his handling of the talks and want time to consider the text of any proposal before it is introduced to the chamber floor.
The legislative window to pass a new law is narrowing as November’s mid-term elections loom, but the lead Democratic negotiator said he was still hopeful the bill could go to a vote next week.
A bipartisan group of senators has been working to draft the text of a bill for lawmakers to vote on before they leave for a two-week 4 July recess.
But they have become bogged down in recent days, as Democrats and Republicans disagree on provisions that would strip certain Americans of their guns.
Mr Cornyn told reporters on Thursday that now is the time for action: “I don’t know what they have in mind, but I’m through talking.”
Earlier in the day, he warned that time was running out to reach an agreement.
“We’re about run out of our rope here, and we got to make some final decisions today if we’re going to be able to get this on the floor next week,” he told radio host Hugh Hewitt.
Connecticut Democrat Chris Murphy and North Carolina Republican Thom Tillis told reporters later on Thursday that the group was still inching towards an agreement.
“To land a deal like this is difficult. It comes with a lot of emotions,” said Mr Murphy, who is leading the Democratic negotiations.
“It comes with political risk to both sides. But we’re close enough that we should be able to get there.”
Senators say disagreements remain over incentives for states to enact so-called red flag laws, which allow police to seize guns from people deemed dangerous. Talks are also ongoing to close the “boyfriend loophole”, which permits abusive partners to buy guns.
If both the Senate and House of Representatives can agree on a bill, it would go to President Joe Biden’s desk to be signed into law.
President Biden has said the plans are a step in the right direction but fall far short of what he called for.
Despite the high rate of firearms deaths, many people in the US cherish their gun rights, which are protected by the Constitution’s Second Amendment to “keep and bear arms”.
These are the first gun safety laws in decades to receive this level of bipartisan support, with previous Democratic attempts at strengthening controls frustrated by Republicans.
Similar efforts in the wake of a previous school shooting at Sandy Hook in Connecticut nearly a decade ago – in which 20 children and six adults were killed – failed to get the required number of votes in Congress.
The Senate, or upper chamber of Congress, is currently split – with 50 Democrats and 50 Republicans – and legislation must have 60 votes to overcome a blocking manoeuvre known as the filibuster.
Ten of the 20 senators who proposed the measures are Republicans, meaning the new legislation could reach that threshold.