Biden looks to promote his plan to reduce gun violence, as he focuses on embattled pieces of his agenda.

President Biden will meet at the White House on Monday with a group of federal and local leaders to promote his administration’s strategy to combat an alarming rise in gun violence, kicking off a week in which he will focus on trying to shore up several domestic priorities that are confronting daunting challenges in Congress.

Unveiled late last month, Mr. Biden’s plan largely encourages jurisdictions across the country to do what they can to bring down crime as hopes for federal legislation grow dim. It includes urging local agencies to draw on $350 billion in funds from his $1.9 trillion coronavirus relief package to support law enforcement. Mr. Biden has also directed the Bureau of Alcohol, Tobacco, Firearms and Explosives to more quickly revoke the licenses of gun dealers who fail to run background checks.

But as the White House seeks to combat a surge in violence — homicides rose 30 percent and gun assaults 8 percent in large American cities last year — the issue is politically freighted for Mr. Biden.

Republicans have accused him of being soft on crime. But as a presidential candidate, he declined to embrace calls from the progressive wing of his own party to defund police departments after police shootings of African Americans. And as president, he has called for more investment in law enforcement agencies.

Mr. Biden has called on Congress to pass measures that would close background-check loopholes, restrict assault weapons and repeal gun manufacturers’ immunity from lawsuits, but there is little appetite for a bipartisan gun control effort. And David Chipman, Mr. Biden’s nominee to lead the Bureau of Alcohol, Tobacco, Firearms and Explosives, faces slim odds as his confirmation process drags on. Mr. Chipman, a two-decade bureau veteran, has a record of taking on the gun lobby in confrontational and unapologetic terms.

On Tuesday, Mr. Biden will travel to Philadelphia to promote another embattled element of his domestic agenda: He is scheduled to “deliver remarks on protecting the sacred, constitutional right to vote,” according to the White House.

After an expansive effort to overhaul the country’s voting laws failed in the Senate, the White House has turned to civil rights groups and advocacy organizations to try to ratchet up political pressure from communities that will be most affected by a Republican-led effort to roll back voting protections in many states.

Although Mr. Biden’s advisers say he is deeply committed to the issue, he is now focusing on finding ways forward that do not necessarily rely on Congress. Vice President Kamala Harris, who is leading the administration’s efforts to expand voting rights, said last week that the Democratic National Committee would invest $25 million in voter outreach and litigation.

Such efforts would appear to fall far short of the changes and protections in the Democrats’ voting legislation. But despite holding several meetings with Democrats and civil rights groups, Mr. Biden, a Senate traditionalist, has avoided discussion on rolling back the filibuster, the legislative mechanism requiring a supermajority in the Senate that Republicans used to block the voting bill.

On Wednesday, Mr. Biden will turn to yet another domestic topic that needs his attention: a centrist infrastructure proposal that, after lengthy negotiations with Republicans, amounts to about 40 percent of what he had proposed to spend for broadband, electric vehicles and water infrastructure. Mr. Biden will meet at the White House with a bipartisan group of governors and mayors to highlight the particulars of the plan.

That proposal and a companion bill in which Democrats plan to address their other economic priorities will face difficult paths through Congress, given the party’s narrow majorities and the sheer ambition of the legislation.