A group of Senate Republicans announced a $928 billion counteroffer on infrastructure on Thursday, a marked increase from their initial proposal. But their offer is still significantly smaller than the slimmed-down alternative to President Biden’s original massive proposal and is focused solely on physical infrastructure needs that do not incorporate the president’s priorities on bolstering “human infrastructure.” The proposal by a group led by Senator Shelley Moore Capito responds to some of the concerns raised by Mr. Biden during their meeting with him at the White House earlier this month. The Republicans had previously come back with a counteroffer of $568 billion, which many Democrats dismissed as too small. Their new offer raises funding levels by $257 billion. “Senate Republicans continue to negotiate in good faith,” Capito said in a press conference on Thursday. “We believe that this counteroffer delivers on what President Biden told us in the Oval Office that day, and that is to try to reach somewhere near $1 trillion over an eight year period of time.” The proposal includes $506 billion for roads, bridges and “major projects” — including $4 billion for electric vehicle infrastructure, $800 million for “reconnecting communities,” and $14 billion for resilience, according to a fact sheet provided by Capito’s office. Mr. Biden has made electric vehicle and other climate-related infrastructure a key priority. The new Republican offer would increase baseline spending for roads and bridges by $91 billion; water infrastructure would see a $48 billion increase, for a total of $72 billion, and there would be a $22 billion increase over baseline spending for passenger and freight rail, bringing proposed funding on this up to $46 billion, according to the fact sheet. The proposal also contains a one-time increase of $25 billion for airports, raising the total to $56 billion, as well as an additional $6 billion for water storage in the West — raising that total to $22 billion. The GOP measure also includes $98 billion for public transit, $22 billion for ports and waterways and $65 billion for broadband infrastructure, a priority for both parties. Under this proposal, $21 billion would be spent on safety and $20 billion on infrastructure financing. The group of Republicans has suggested using unspent funds from previous coronavirus relief plans to pay for the infrastructure bill. “We do believe that this money is available. If they have a different theory then they’ve got to show us the numbers,” Senator Pat Toomey said on Thursday of the unused funding. Capito noted that several states will not be accepting monies for additional unemployment benefits, which could also be used to pay for an infrastructure proposal. Some Republicans have also floated user fees, though this idea is unpopular with Democrats. The Republicans say that Democrats can either accept their bipartisan proposal — or try to ram a larger bill through without any Republican support. Capito noted that the Senate Environment and Public Works Committee had recently approved two smaller infrastructure bills on a bipartisan basis, indicating that other priorities for the White House could be addressed in different, smaller legislation. GOP Senator Roy Blunt said that Mr. Biden told the group that if Republicans wanted to break up infrastructure priorities into smaller bills, the president said, “I’ll try to get the rest of it in some other way.” Blunt also noted that this would be the “biggest infrastructure bill ever put on a president’s desk by a Congress.” The White House proposed a $1.7 trillion counteroffer on infrastructure to Senate Republicans last week, roughly half a billion dollars less than Mr. Biden’s initial $2.3 trillion proposal. However, Republicans said the most recent offer still included provisions that they don’t consider to be related to “traditional” infrastructure needs, such as provisions on construction of veterans hospitals and on strengthening home care. Mr. Biden had also proposed paying for a large infrastructure bill by raising the corporate tax rate to 28%, which Republicans oppose. The 2017 tax cuts bill signed by former President Trump lowered the corporate tax rate to 21%. Meanwhile, GOP Senator Mitt Romney is leading a separate bipartisan group of eight senators who are also working on an infrastructure proposal. Romney told reporters on Wednesday that Capito’s group was the “front burner” of negotiations, and that his group was on the “back burner.” His group is considering a proposal of “not quite a trillion.” Senate Majority Leader Chuck Schumer indicated on Tuesday that, regardless of whether Republicans and Democrats come to an agreement, the Senate will move forward with infrastructure legislation in July. Mr. Biden has also proposed a $1.8-trillion American Families Plan, which is focused on “human” infrastructure, with provisions on health care, child care and education. This proposal has also been received with skepticism by Republicans.