House Speaker Nancy Pelosi and Senate Minority Leader Charles E. Schumer on Wednesday laid down markers for what congressional Democrats want to see in the next legislative package in response to the coronavirus pandemic, including more money for small businesses, hospitals and local governments.

The leaders said Democrats do support $250 billion in assistance to small businesses, in line with what Republicans have called for, though Mrs. Pelosi and Mr. Schumer want at least $125 billion directed through “community-based” financial institutions that serve underrepresented communities.

They also want $100 billion for hospitals and health systems that would go toward national rapid testing and personal protective equipment, $150 billion for state and local governments, and a 15% increase to the maximum SNAP, or food stamp, benefit.

“After we pass this interim emergency legislation, Congress will move to pass a CARES 2 Act that will extend and expand the bipartisan CARES Act to meet the needs of the American people,” Mrs. Pelosi, California Democrat, and Mr. Schumer, New York Democrat, said in a joint statement.

They said “CARES 2” needs to provide “transformational relief” to the American people.

The $2.2 trillion rescue package Congress recently cleared was also referred to as the CARES Act.

Senate Majority Leader Mitch McConnell on Tuesday said he was working with Mr. Schumer and Treasury Secretary Steven T. Mnuchin to win approval for an additional $250 billion for a small business lending program that was part of the $2.2 trillion legislation.

Mr. McConnell said he wanted to approve additional money for the program via unanimous consent or voice vote during the next scheduled Senate session on Thursday.