ALBANY – Democrats in the Senate here are predicting they will put a “serious dent” in the Republicans’ majority this November based on the results of Tuesday’s primary elections.

The minority leader, Senator David Paterson of Harlem, said yesterday he anticipates gaining at least two seats now that his preferred candidates have secured the Democratic nominations.

Jeffrey Klein won in the 34th district, formerly held by Republican Guy Velella of the Bronx; and Jose Serrano took the 28th district, occupied by Senator Olga Mendez of Spanish Harlem, who switched to the GOP two years ago.

If Democrats win those races and hold off Republican challengers elsewhere, the Republican majority that began the year at 38-24 – before Velella’s conviction on bribery charges – would shrink to 36-26 next January.

Mr. Paterson calls that a first step in a long-term plan for Democrats to take control of the Senate – and therefore both houses of the Legislature – for the first time since 1965.

Although Democrats outnumber Republicans 5.3 million to 3.1 million in New York, the GOP has controlled the Senate every year but one since 1938.

After a year in which the Legislature spent much of its session in gridlock, passed the latest state budget in history, and missed a court deadline to overhaul education funding, Mr. Paterson said Senate Democrats are well positioned to capitalize on voters’ desire to shake up state government.

“We need to turn over a new tree and totally change the way we do business,” he said. “To take the majority in the Senate, we recognize we not only have to beat the Republicans, we have to beat the Albany culture.”

The majority leader, Senator Joseph Bruno of Rensselaer County, pointed out in a statement that Republican incumbents swept all six of the primary challenges against them.

Tacitly acknowledging a setback, Mr. Bruno congratulated the Republican nominee in the 34th District, John Fleming, for running a “spirited campaign.” Mr. Bruno’s preferred candidate, Assemblyman Stephen Kaufman of the Bronx, lost both the GOP primary to Mr. Fleming, 43% to 57%, and the Democratic primary to Mr. Klein, 35% to 58%.

Mr. Kaufman, a lifelong Democrat, was expected to join Mr. Bruno’s majority if elected, and Republicans spent hundreds of thousands of dollars trying to swing the Democratic primary their way.

“My victory is the first large chink in the armor of Joe Bruno,” Mr. Klein said.

Although Mr. Kaufman won the Conservative primary, and also has the nomination of the Independence Party, it was unclear yesterday whether he will remain in the race.

Mr. Bruno wasn’t the only legislative leader stung by the primary results. Two Assembly Democrats went down to defeat, including one targeted by the “Fix Albany” campaign of the Nassau County executive, Thomas Suozzi. A Glen Cove councilman supported by Mr. Suozzi, Charles Lavine, defeated incumbent Assemblyman David Sidikman, 52% to 48%. Mr. Suozzi, a Democrat who blames Albany for passing budgets that drive up local property taxes, called Mr. Lavine’s win “the shot heard ’round the state.”

“We’ve sent a clear message regarding the Democratic Assembly,” he said. “Now we’re going to the Republican state Senate.” His Fix Albany political action committee is endorsing challengers against two GOP senators in Nassau County, Carl Marcellino and Dean Skelos.