WASHINGTON – The Texas Supreme Court justice, Priscilla Owen, won Senate confirmation as a federal appeals judge yesterday after a ferocious four-year battle, a personal triumph that also marked a victory for President Bush in his drive to install conservatives on the nation’s highest courts.

The 56-43 vote was largely along party lines and made the 50-year-old jurist the first of Mr. Bush’s long blocked nominees to win approval under a newly minted agreement by Senate centrists meant to end years of partisan gridlock.

“We cannot stop with this single step,” Majority Leader Frist said in a written statement soon after the vote. Dr. Frist, a Republican of Tennessee, resurrected a threat to strip Democrats of their right to filibuster Mr. Bush’s picks for the nation’s highest courts if they violate the two-day-old accord.

“We must give fair up-or-down votes to other previously blocked nominees. It is the only way to close this miserable and unprecedented chapter in Senate history,” he said.

The Democratic leader, Harry Reid, said he was “ready to put all this behind us and move on.”

“I would hope the president would move on,” he added later at a news conference in which Democratic leaders urged renewed attention to the economy, health care, defense, and other issues.

For his part, Dr. Frist told reporters he intended to seek votes early next month for Janice Rogers Brown and William Pryor, two other nominees long blocked by Democrats but now protected by Monday night’s bipartisan agreement.

In addition, the Senate’s top Republican said he would press for votes on the nominations of William Myers and Henry Saad – two of the president’s selections who were not guaranteed final votes in the centrists’ deal.

Republican officials also said they expected Dr. Frist to push for votes on Brett Kavanaugh and William Haynes. Both are appeals court nominees strongly opposed by Democrats who have yet to clear the Senate Judiciary Committee.

Beyond that, there is a widespread expectation that one or more Supreme Court vacancies will occur in the coming months, any one of which has the potential to reignite partisan warfare over the future of the judiciary.

Mr. Reid, the Democratic leader from Nevada, sounded less than eager to continue debating judicial nominees opposed by many senators in his party as well as independent groups aligned with his party.

The final debate over Justice Owen’s nomination was utterly without suspense following Monday’s 81-18 vote to advance her nomination to the brink of confirmation.

Since her original nomination in 2001, to the 5th U.S. Circuit Court of Appeals in New Orleans, Democrats have argued that Justice Owen has displayed a tendency for judicial activism, allowing her own political beliefs to color her rulings. In particular, they pointed to an abortion-related case in which she sided with a minority of the court that wanted to make it harder for teens to have an abortion without parental permission.

Republicans countered that such claims were politically motivated, and noted she easily won election to the Texas Supreme Court in 1994 and reelection in 2000.

Justice Owen was one of 10 first term appeals court appointments made by Mr. Bush who were denied votes by Democratic filibusters.