President Trump said on Friday that he would not sign a major bipartisan housing bill, a decision he framed as a protest against Senate Republicans for failing to pass an unrelated voting restriction bill that does not have enough support to clear the Senate.

“I will not sign the Housing Bill, which has been fully approved by Congress and sent to the White House, in PROTEST over the fact that the United States Senate is not capable of passing THE SAVE AMERICA ACT,” Mr. Trump wrote on social media, referring to the elections bill.

Mr. Trump’s decision appears to be symbolic. The measure, the first major legislative effort to address the nation’s housing crisis in more than three decades, will become law at midnight even without his signature unless he vetoes it, which he did not say he would do.

But Mr. Trump’s pronouncement is still a remarkable dismissal by a president of efforts by his own party to address a major political vulnerability. And it reflected the growing rift between the president and Senate Republicans over the elections bill, which contains strict voter identification requirements and a raft of other measures the president has demanded.

The housing measure adjusts a host of federal regulations to make it easier and cheaper to build housing. That approach won broad support from economists and policy experts, and the bill passed Congress last month with overwhelming bipartisan support, an increasingly rare accomplishment in a starkly polarized legislature.

The bill, known as the 21st Century ROAD to Housing Act, was poised to deliver congressional Republicans a significant victory ahead of November’s midterm elections, as they try to blunt Democrats’ attacks over rising costs.

But Mr. Trump clouded the achievement. Hours before a planned signing ceremony at the Capitol last month that he abruptly canceled, he dismissed the bill as “of minor importance” and said he would sign it only if Congress passed the voting measure.

Mr. Trump’s focus on the elections bill has already derailed Republicans’ congressional agenda. House leaders were forced to scrap votes twice last month after a group of far-right lawmakers refused to let legislation come to the floor unless the Senate took action on the voting measure.

Most Republicans back voter identification requirements, though Mr. Trump’s restrictions are far greater. The bill would require Americans to show proof of citizenship to register to vote and would severely curtail voting by mail, a popular practice in many Republican-held states and districts.

Senate Republicans, including the majority leader, Senator John Thune of South Dakota, have repeatedly said they do not have the 60 votes needed to overcome a Democratic filibuster against the bill. They have also acknowledged that there is not enough support in their caucus to overhaul the filibuster and find a way to push the bill through over Democratic opposition.

Republican leaders did not expect Mr. Trump to block the housing bill, and Speaker Mike Johnson sent it to his desk on June 29, starting a 10-day clock for the president to sign the bill, veto it or allow it to automatically become law.

Still, the president’s approach, in which the bill effectively limps across the finish line, robbed congressional Republicans of the fanfare they had sought to help make their case to voters that they were addressing affordability. Polls show that it is a top concern and that Americans increasingly blame them for economic woes.

Though Republicans are expected to trumpet the housing legislation on the campaign trail, they will do so after weeks in which Mr. Trump — who last month issued a proclamation calling the bill “comprehensive and consequential” — publicly downplayed it as a “yawn” compared with his elections measure.

Democrats have seized on Mr. Trump’s remarks to bolster their arguments that the president is unresponsive to, if not outright dismissive of, Americans’ concerns about affordability. Mr. Trump has described the issue as a “hoax” or a “con job.”

The bill aims to expand the housing supply to eventually drive down prices for buying a home or renting. It would relax federal regulations, including environmental reviews, to make construction faster and cheaper. It would also ease lending rules and include incentives for state and local governments to build new homes.

Though Mr. Trump at times weighs in publicly on legislative negotiations, he had been relatively hushed on the housing package. Still, the final bill included a provision intended to win support from the president: a limit on some large investors that snap up single-family homes.

That policy, something Mr. Trump tried to address in an executive order this year, proved to be one of the biggest flash points in negotiations between the House and the Senate.

Yet Mr. Trump has not discussed the provision much since the legislation passed. Instead, he has diminished its importance by arguing that the most effective way to lower housing costs would be a reduction in interest rates that could help to push down mortgage bills. The new chairman of the Federal Reserve, Kevin M. Warsh, has expressed optimism about taming inflation but has not committed to quickly lowering interest rates.