In the latest example of divisions among congressional Democrats over voting rights, four House Democrats emailed the party caucus on Thursday pushing for their colleagues to muscle through two election bills now being considered on Capitol Hill, arguing that “democracy is on the line.”

The email, which was signed by Representatives Mondaire Jones of New York, Val Demings of Florida, Nikema Williams of Georgia and Colin Allred of Texas, represented not-so-subtle pushback to recent statements from influential Democrats like Senator Joe Manchin III of West Virginia and Representative James E. Clyburn of South Carolina, who have each expressed to the caucus a preference for a more narrow strategy.

The most ambitious legislation Democrats have put forward is the For the People Act, a sweeping bill to overhaul the nation’s elections system that would protect voting rights, reduce the role of money in politics, strengthen enforcement of existing election laws and limit gerrymandering. They have also introduced the narrower John Lewis Voting Rights Act, which would restore crucial parts of the 1965 Voting Rights Act that were struck down by the Supreme Court in 2013, including the preclearance requirements under which some states mostly in the South had to receive federal approval before changing their election laws.

The email from the four representatives argues that passing only the John Lewis Act — which Democrats like Mr. Manchin and Mr. Clyburn have recently told other members they would prefer — would be an insufficient response to the spate of voting restrictions Republicans have enacted across the country since the 2020 presidential election. The email states that passing the narrower bill alone would leave too much up to the courts, do little about laws already enacted, do nothing to reduce partisan gerrymandering, and would still be no closer to Senate passage.

“John Lewis’s final fight was to champion both the For the People Act that contains his Voter Empowerment Act and the Voting Rights Act that now bears his name,” the email states, invoking the name of the Georgia representative and civil rights icon, who died last year. “Not since the Jim Crow era have we seen laws explicitly aimed at suppressing the votes of Black, Brown, and young Americans like those being considered in state capitals across the nation right now.”

“Any proposal that shuns H.R. 1 in favor of nationwide preclearance alone is either dangerously naïve or simply misinformed about what is happening in states across the country,” the email reads. “Time is running out.”

Mr. Clyburn and other members of the Congressional Black Caucus have privately expressed discomfort with independent redistricting commissions. Those commissions would eliminate gerrymandering, which has been a thorn in the side of Democrats seeking to win swing districts but has also helped spur the rise of Black representation throughout the South, packing large numbers of Black voters into single urban districts.

President Biden has frequently emphasized the importance of voting rights legislation, but has yet to weigh in on which bill he would prefer to reach his desk, if not both. The measures are both unlikely to pass the Senate, where Republicans broadly oppose them, unless Democrats alter the Senate filibuster rule that requires 60 votes to advance legislation.