For years, Democrats in Iowa and New Hampshire have battled criticism from others in the party who argued that the two states are not racially diverse enough to kick off the Democratic nomination process.

But after a disastrous 2020 cycle, in which Iowa officials struggled to tabulate votes and neither state proved predictive of President Biden’s eventual victory, Democratic leaders are exploring with new urgency whether to strip the two states of what has been a priceless political entitlement: their traditional perch at the start of the party’s presidential calendar.

Several ideas are expected to be heard on Friday by the Democratic National Committee’s rules and bylaws committee, which governs the nominating process. One calls for an application process for states based on several criteria, including diversity. Another idea, raised at a meeting in January, would consolidate all four of the current early-voting states — Iowa, New Hampshire, South Carolina and Nevada — into a single first voting day before Super Tuesday.

The debate has taken on new urgency in response to a steady drumbeat of criticism by activists, elected officials and some members of the rules and bylaws committee. The concerns raised include fears that Iowa’s caucus system disenfranchises some voters and that neither Iowa nor Hampshire is racially diverse enough to act as a stand-in for the Democratic voting base.

In the last election cycle, logistical challenges including late-arriving votes and inaccurate data also highlighted the shortcomings of Iowa’s caucus process and muddied its ability to name a winner.

“To me it’s not about one state, it’s not about punishing,” said Mo Elleithee, a former spokesman for the Democratic National Committee and for Hillary Clinton who serves on the rules and bylaws committee.

“We have a chance to show our values in our process,” Mr. Elleithee said. “Diversity, inclusion, and, given the job of the D.N.C. is to elect Democrats, by putting our people in front of as many battleground states as possible.”

Members of the rules and bylaws committee, several of whom did not respond to requests for comment, have been told to expect to work on the issue throughout the summer with the intention of setting a firm nomination calendar by the fall.

“We are not close to making a decision,” said Donna Brazile, a former chair of the Democratic National Committee who also serves on the rules and bylaws committee. On Friday, she said, “we start the conversation.”

In January, during a virtual meeting of the same body, Mr. Elleithee and others made the case for overhauling the nominating calendar and were met with relatively little pushback — which some members took as a sign that even the delegations from Iowa and New Hampshire recognized that some change may be inevitable.

State officials in Iowa and New Hampshire have fiercely resisted previous proposals to downgrade their primacy in the party’s nominating calendar, publicly and privately whipping allies to their side, but they have not yet begun to do so, according to committee members. Still, they said that any change to the system would be expected to demonstrate the party’s acknowledgment of the importance of smaller states and rural voters.

Scott Brennan, an Iowan who sits on the rules and bylaws committee, did not respond to a request for comment but argued at the January meeting that Iowa’s small-state status has allowed barrier-breaking politicians to thrive.

“Barack Obama was able to come to Iowa, the little-known senator from Illinois, and ultimately become the nominee,” Mr. Brennan said then.

Mr. Brennan also referenced Pete Buttigieg, the former mayor of South Bend, Ind., who is now the secretary of transportation. When Iowa’s caucuses were eventually tabulated in 2020, Mr. Buttigieg became the first openly gay candidate to win a presidential primary or caucus, with a narrow victory over Senator Bernie Sanders of Vermont.

“Folks like that have chances to really shine,” Mr. Brennan said. “If Iowa is not first in the process, I think that goes away.”

Ms. Brazile, who in 2000 became the first Black woman to direct a major presidential campaign, said the party benefited when states like Nevada and South Carolina were added to the early nominating schedule to improve the representation of Black and Latino voters.

“It’s very important that our primary calendar reflect those values,” Ms. Brazile said at the rules and bylaws committee meeting in January. “We need to thank South Carolina and Nevada for giving us quality nominees over the years. That diversity has uplifted the party and also the values we hold as American citizens.”

Previous efforts to change the nomination calendar to minimize the importance of Iowa and New Hampshire have hit political roadblocks. Ambitious elected officials, often eyeing the next presidential cycle, have sought to avoid upsetting state officials in Iowa and New Hampshire, who have historically guarded their first-in-the-nation status with extreme urgency. Presidents have often felt indebted to voters in those states, quelling criticisms before they reach the highest levels of the party.

But Mr. Biden owes no such obligation. In 2020, he became the first modern Democrat to win the party’s presidential nomination without winning either in Iowa or New Hampshire. On the night of the New Hampshire primary — where Mr. Biden finished fifth — he fled to South Carolina and argued against the importance of Iowa and New Hampshire, highlighting the dearth of Black voters in those states as a reason the results should be downplayed.

“Tonight, I’ve just heard from the first two states, not all the nation,” Mr. Biden said at the time. “Up till now, we haven’t heard from the most committed constituency in the Democratic Party — the African American community.”

He went on to win the South Carolina primary in a landslide.