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MIAMI – In a state where legal action often goes hand in hand with presidential elections, the Florida Democratic Party filed a federal lawsuit early Sunday to force the state government to extend early voting hours in South Florida.

The lawsuit was filed after a stream of complaints from voters who sometimes waited nearly seven hours to vote or who did not vote at all because they could not wait for so long to do so.

Shortly after the lawsuit was filed, local election supervisors in Miami-Dade and Palm Beach Counties, where lines sometimes snaked out the door and around buildings, said they would allow voters to request and cast absentee ballots on Sunday. Voters in three other Florida counties will also be able to pick up and drop off absentee ballots. State election law permits election offices to receive absentee ballots through Tuesday as long as they are cast in person.

But later on Sunday, Miami-Dade’s county election supervisor closed down the line for absentee ballots after two hours at its Doral office. It was eventually reopened, and election officials said that anyone in line by 5 p.m. would be able to drop off a ballot.

In response to a separate Democratic Party lawsuit in Orange County, where Orlando is the biggest city, a judge extended early voting on Sunday after a polling station at the Winter Park library was forced to shut down over a suspicious package. The extra hours were being offered at only one polling station.

In the South Florida suit, filed in Miami, Democrats argued that an emergency order was needed to “extend voting opportunities” before Tuesday in Miami-Dade, Broward and Palm Beach Counties. They also urged that voters be allowed to cast absentee ballots in person in the counties’ main election offices. The three counties are home to about 32 percent of the state’s registered Democrats.

With the election two days away, a judge will have little time to act. But by going to court, Democrats are hoping to either get a ruling or to pressure officials in Broward County — the holdout among the three — into accommodating people who want to cast absentee ballots in person on Monday, according to a senior Democratic Party official. At the same time, lawyers across Florida are preparing to closely monitor voting on Tuesday.

The lawsuit states that the three counties have “inadequate polling facilities” and have failed to meet the needs of voters. Some voters faced “prohibitively long” lines and did not finish voting until early Sunday morning.

“The extraordinarily long lines deterred or prevented voters from waiting to vote,” the lawsuit states. “Some voters left the polling sites upon learning of the expected wait, and others refused to line up altogether. These long lines and extreme delays unduly and unjustifiably burdened the right to vote.”

With complaints streaming in from angry voters, the Florida Democratic Party and the League of Women Voters asked Gov. Rick Scott and state election officials on Thursday to extend early voting. They argued that some voters were leaving without voting because they did not have all day to wait in line. The Monroe County election supervisor, Harry Sawyer, also asked Mr. Scott to use his emergency powers to extend early voting.

But the governor and state elections officials turned down the request, saying that the process was running smoothly and that the move was unnecessary.

Last year, Mr. Scott and the Republican-controlled Legislature pushed through a measure to cut early voting from 14 days to 8 days and to cancel voting on the final Sunday before Election Day. Because more Democrats cast early ballots than Republicans, the move was viewed by Democrats as an effort to blunt Democratic turnout.

The long lines have been particularly acute in South Florida, which is the state’s most densely populated area and which has one of the longest ballots this year. In Miami-Dade County some voters had to scour complicated 12-page ballots.

The Miami Herald reported that the last early vote in Miami-Dade County was not logged in until 1 a.m. Sunday. The county had said it would honor the votes of people who were standing in line at 7 p.m. Saturday.

Some election supervisors had warned that the combination of long ballots, fewer voting days and fewer polling stations would lead to unreasonably long lines.

State elections officials reported that by Saturday night, 3.9 million Floridians had either cast absentee ballots or voted early.

“Because of Governor Scott’s refusal to follow precedent and extend early voting hours in the face of unprecedented voter turnout in South Florida, we are requesting in federal court that more Floridians have a meaningful chance to early vote,” said Rod Smith, the chairman of the Florida Democratic Party.

Michael Cooper contributed reporting.