It was not quite the blue wave that Democrats in New York had hoped for, but the results of Tuesday’s special elections in 11 state legislative seats did give the party hope that they might be able to help national Democrats retake the House of Representatives in the fall.

Perhaps the brightest result for Democrats was in a highly contested race for State Senate in Westchester County, where the Democratic candidate, Assemblywoman Shelley B. Mayer, defeated the Republican, Julie Killian, by 15 points.

And, as was expected, Democrats easily kept the vacant Assembly seats in their column in races in the Bronx, Manhattan and Queens, where the party enjoys a giant surplus in voter registrations.

But the picture outside the city was mixed, where expectations for a blue wave felt more like a ripple. On Long Island, for instance, where three Assembly seats were vacated by Republicans, the special election kept two of those districts red.

The third, in Suffolk County, was a notable exception: In the 10th Assembly District, Steve Stern, a Democrat and former county legislator, won a seat that had been in Republican control for 40 years.
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In two other Assembly races outside Albany, formerly Republican seats stayed that way — but just barely. In both the 102nd and 107th Districts in the capital region, the Republican challengers eked out victories, edging out their Democratic rivals by only 200 to 300 votes.

And in the Buffalo area, where the Assembly contest pitted two registered Democrats against each other — one on the Democratic line and the other on the Republican line — the challenger with Republican backing won the election.

State Republicans, perhaps fearing a far worse outcome, cheered the results. In a phone interview, Edward F. Cox, chairman of the state Republican Party, said that, with the exception of New York City and its closest suburbs, the “bottom line is that the national blue wave is muted.” He added: “Upstate and on Long Island, we’re doing very well. The elections showed that if you put out good candidates, except in a few areas, we win.”

Steve Stern, left, a Democrat, and Rich Schaffer, the chairman of the Suffolk County Democratic Party, celebrated Stern’s victory in the special election for the 10th Assembly District seat. Credit Barry Sloan/Newsday
Even some longtime Democratic political consultants said the results were a cautionary tale for Democrats. “What these elections prove is that locations that were heavily Republican are likely to remain that way,” said Hank Sheinkopf, a veteran Democratic strategist.

“It also highlights the great divide between New York City and upstate New York,” he added. “It’s not impossible that the red congressional districts will remain red because they are a lot like the Assembly districts. Based on these results, it’s going to be tougher for the Democrats to flip these congressional seats than they think.”

But Democratic officials in New York saw the outcomes very differently.

Geoff Berman, the executive director of the state’s Democratic Party, said the flipping of the Long Island Assembly seat, the margin of Ms. Shelley’s victory (the widest in memory), and the narrowing of Republican wins upstate forecast a positive outlook for the midterm elections this fall.

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Mr. Berman said the party’s twin goals in November were switching a half-dozen competitive congressional districts from red to blue, and delivering an unassailable Democratic majority in the State Senate. “We want to put the brakes on the Trump train,” he said, “and these results show that we are on track to do that. We are winning by greater margins in the districts we have won.”

While disappointed that they did not win two Assembly districts near Albany, Democratic officials pointed out that President Trump won those by strong margins in 2016.

With more than 15,000 votes cast in the 107th Assembly District, the Democratic candidate, Cindy Doran, a retired teacher and county legislator, lost to Jake Ashby, an Army veteran and county lawmaker, by fewer than 300 votes. The district encompasses parts of Washington, Rensselaer and Columbia Counties, with the latter two supporting Mr. Trump in 2016.

Downstate, the victory by Mr. Stern in the 10th Assembly District was dictated as much by Democratic turnout as the dynamics of the race itself. Even though the last time a Democrat occupied the seat was four decades ago, Democrats outnumber Republicans in the district by nearly 6,000 registered voters.

Barbara Malleck, a registered Democrat and a past president of the local League of Women Voters, said she showed up at her local firehouse in Huntington and found a long line of people waiting to vote. “I was amazed at the turnout,” she said on Wednesday.

Despite the Democrats’ strong showing in Suffolk County, Republican strategists gleaned a sanguine subtext from the party’s losses and narrow victories. “It shows that Republican bleeding may be limited to the suburbs,” said William F. B. O’Reilly, a political consultant and a partner in the November Team. “November will challenge this thesis of course, but this gives Republicans some hope.”