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Washington — House Speaker Nancy Pelosi said Sunday she is looking to advance the bipartisan infrastructure bill and a broader $3.5 trillion budget framework simultaneously, an effort to keep House Democrats united as the chamber prepares to take up the plans.

Pelosi said in a letter to her Democratic colleagues on Sunday that she asked the House Rules Committee to “explore the possibility” of a rule, which governs floor debate, that moves forward the budget resolution and bipartisan infrastructure bill. Both measures passed the Senate last week.

“This will put us on a path to advance the infrastructure bill and the reconciliation bill,” the California Democrat said.

Pelosi said her plan is for the House to pass the $3.5 trillion budget resolution the week of August 23, which would then pave the way for the Democratic-controlled House to approve its sweeping reconciliation bill encompassing President Biden’s priorities for health care, child care and education “as soon as possible.”

Pelosi’s plan to tie the bipartisan infrastructure bill with the budget resolution comes after a group of nine moderate Democrats told her last week they wouldn’t vote for a budget resolution until the bipartisan infrastructure plan passes the House and is signed into law.

But her effort to move the two simultaneously has already fallen flat with the moderate Democratic lawmakers, who reiterated in a statement later Sunday that their view was unchanged: vote first on the bipartisan bill swiftly and then consider the budget resolution.

“As the president echoed after the infrastructure bill passed the Senate, we must get shovels in the ground and people to work,” they said, adding the nation “simply can’t afford any delays.”

The pushback from moderate Democrats over how to proceed with moving the two measures complicates Pelosi’s initial plan for the House not to vote on the bipartisan bill until the Senate passes the larger $3.5 trillion legislative package.

Progressives, meanwhile, have said they won’t back the bipartisan infrastructure plan until the broader legislation addressing social programs clears the upper chamber.

The House is set to cut its August recess short and return to Washington next week to begin its work on the two proposals.

The Senate approved the infrastructure bill with bipartisan support, a major victory for Mr. Biden as he looks to enact his economic agenda. Its passage was the culmination of months of negotiations between the White House and a bipartisan group of senators. The plan includes $550 billion in new spending to revitalize the nation’s roads, bridges, railways and ports.

The upper chamber then passed a budget resolution along party lines, which clears the way for it to craft its massive $3.5 trillion measure. Democrats are using a process called budget reconciliation to approve the sweeping plan, which allows the spending package to pass the Senate without GOP support.

The budget resolution is the second plank of a two-track strategy employed by Democratic leaders to enact Mr. Biden’s economic priorities.

Zak Hudak and Kris Van Cleave contributed to this report