With the midterm election cycle fast approaching, Republicans in the key states of Florida and Ohio have made critical progress in their push to add to their dominance on congressional maps by carving new districts that would be easier for G.O.P. candidates to win.

In Florida, Gov. Ron DeSantis on Tuesday vetoed congressional maps drawn by the Republican-controlled Legislature and called for a special session to draw new maps in mid-April, a rare fracture between the Republican governor and state lawmakers. Mr. DeSantis had previously pledged to veto the maps and had pushed his own maps that would have given his party a stronger advantage in the state’s congressional delegation.

In Ohio, a new map of congressional districts that is gerrymandered to heavily favor Republicans appeared highly likely to be used in the midterm elections after the State Supreme Court indicated on Tuesday that it would not rule on a challenge to the map until after the May 3 primary election.

The Republican pressure comes as Democrats have fared better than expected in this year’s redistricting cycle. Democrats have drawn aggressive gerrymanders in states like New York, Oregon, Illinois and Maryland, while Republicans have sought to make their current seats safer in states like Texas and Georgia.

The result is an emerging new congressional landscape that will not tilt as heavily toward Republicans as it did after the last redistricting cycle, in 2011. In the first elections after that round of redistricting, in 2012, Democrats won 1.4 million more votes for the House of Representatives, yet Republicans maintained control of the chamber with 33 more seats than Democrats.

The realignment in this year’s redistricting has rankled some Republicans across the country, who had called on G.O.P.-led state legislatures to be more aggressive in drawing maps.

“Republicans are getting absolutely creamed with the phony redistricting going on all over the Country,” former President Donald J. Trump said in a statement last month.

Mr. DeSantis seemed to share Mr. Trump’s view, taking the rare step of interjecting himself into the redistricting process and proposing his own maps, twice. His most recent proposal would have created 20 seats that would have favored Republicans, and just eight that would have favored Democrats, meaning the G.O.P. would have been likely to hold 71 percent of the seats. Mr. Trump carried Florida in 2020 with 51.2 percent of the vote.

But Republicans in the State Legislature, who often acquiesce to Mr. DeSantis’s requests, largely ignored the governor’s proposed maps and passed their own maps that would have most likely given Republicans 18 seats, compared with 10 for Democrats. Mr. DeSantis declared the maps “DOA” on Twitter when they passed.

In a news conference on Tuesday announcing his veto, Mr. DeSantis said the map drawn by the Republican-controlled Legislature violated U.S. Supreme Court precedent.

“They forgot to make sure what they were doing complied with the 14th Amendment of the U.S. Constitution,” Mr. DeSantis said at the State Capitol.

The vetoed map did away with a seat held by a Black Democrat, Representative Al Lawson of Tallahassee, and created a smaller district in Jacksonville where a Black Democrat might get elected. Mr. DeSantis had proposed maps earlier this year that further eroded minority representation, including in Mr. Lawson’s district.

Mr. DeSantis acknowledged that the map lawmakers end up drawing in the special session would still be likely to face a court challenge. The state’s current map was drawn by the courts after Florida voters wrote anti-gerrymandering provisions into the State Constitution in 2010.

On Tuesday, the governor appeared to take aim at those provisions, calling them far-reaching and inconsistent. He hinted that in the future, the state might argue in federal court that the provisions were unconstitutional, but he said his intent was not necessarily to repeal them.

“Our goal in this was just to have a constitutional map,” he said. “We were not trying to necessarily plot any type of litigation strategy.”

He added, “We will obviously say it’s unconstitutional to draw a district like that, where race is the only factor,” referring to Mr. Lawson’s heavily Black district in North Florida.

Legislative leaders in Florida told lawmakers to plan to be in Tallahassee for the special session from April 19-22. Florida has a relatively late primary election, set for Aug. 23, and voting is unlikely to be threatened by the uncertainty over the maps. However, some House races have yet to attract a full field of candidates, in part because the district lines remain unclear.

In Ohio, the Republican-friendly map would hand G.O.P. candidates at least 10 of the state’s 15 House seats — and potentially as many as 13 — although fewer than six in 10 votes have favored the party in statewide elections over the past decade.

The Ohio Supreme Court’s decision vindicated what most experts have called a foot-dragging strategy by Republicans who control the state’s General Assembly and have dominated the map-drawing process in the ostensibly bipartisan Ohio Redistricting Commission. The State Supreme Court had rejected an initial version of the congressional map in January, calling it a Republican gerrymander that violated the Ohio Constitution.

Voting rights advocates immediately challenged the second version of the map after the G.O.P. majority on the Redistricting Commission released it in mid-March.

The Ohio Supreme Court has also rejected three successive Republican-drawn maps of districts for the State House and Senate as gerrymanders, once threatening to hold the Redistricting Commission in contempt for slow-walking the mapmaking process. The court appeared likely to do so again after the Redistricting Commission produced a fourth set of legislative maps late Monday that were almost identical to the last ones that the court struck down.

In adopting those maps, Republicans on the commission ignored the recommendations of two outside redistricting experts that the State Supreme Court had chosen to help with the process.

“The entire move was disrespectful of Ohio taxpayers, voters, the Supreme Court and the Ohio Constitution as a shameless power grab,” said Jen Miller, the executive director of the state chapter of the League of Women Voters, one of two groups that have challenged the maps. “But I don’t think they will have the last say.”

Ms. Miller and other experts said the Supreme Court could reopen contempt proceedings against the commission and order a fifth attempt to draw constitutional legislative maps.

The standoff over congressional and legislative maps has made a shambles of a redistricting process aimed at removing politics from mapmaking that Ohio voters resoundingly approved via constitutional amendments in 2015 and 2018.

Those amendments took map-drawing powers away from the State Legislature and gave them to a newly created Redistricting Commission whose current membership is weighted toward Republicans. The amendments require the commission to produce maps that reflect the share of votes each party received in statewide elections over the previous decade — about 54 percent for Republicans and 46 percent for Democrats.

The State Supreme Court has consistently ruled that the commission has violated that mandate.