WASHINGTON — Washington’s nascent debate over gun safety devolved into a partisan round of name-calling on Tuesday, as Democrats and Republicans accused one another of playing politics with a life-or-death issue, dimming hopes for a quick compromise to address the wave of mass shootings that have terrorized the country.

On their first full day back in the Capitol after a lengthy August recess, Democrats sought to intensify political pressure on Republicans to embrace tougher gun restrictions, while also laying the foundation for making gun violence a central issue of their 2020 campaigns should a compromise falter.

House Democrats pushed forward with a new package of gun restrictions, including a bill that would ban the manufacture and sale of large-capacity magazines, and sharpened their calls for Senator Mitch McConnell, Republican of Kentucky and the majority leader, to take up a bill they approved in February expanding background checks to all gun buyers.

But Mr. McConnell insisted, as he has in the past, that he would not take up any legislation unless President Trump agreed to sign it into law. Speaking to reporters at the Capitol, he took aim at his Democratic counterpart, Senator Chuck Schumer, and Speaker Nancy Pelosi, dismissing their demands as a “stunt.” Mr. Trump, he noted, had long ago said he would veto the House-passed background check bill.