A Senate official rejected on Sunday a measure in Republicans’ sweeping domestic policy bill that could limit lawsuits seeking to block President Trump’s executive actions.

The measure would target the preliminary injunctions and temporary restraining orders issued by federal judges on Mr. Trump’s directives. Those rulings have halted or delayed orders on a host of policies, including efforts to carry out mass firings of federal workers and to withhold funds from states that do not comply with demands on immigration enforcement.

The G.O.P. proposal would require parties suing over federal policies to post a bond covering the government’s potential costs and damages from an injunction if the judge’s order were found later to have been wrongly granted.

“Individual district judges — who don’t even have authority over any of the other 92 district courts — are single-handedly vetoing policies the American people elected President Trump to implement,” Senator Chuck Grassley, Republican of Iowa and the chairman of the Judiciary Committee, said in announcing the proposal in March.

Republicans are pushing their bill to carry out President Trump’s agenda through Congress using special rules that shield legislation from a filibuster, depriving Democrats of the ability to block it. But to qualify for that protection, the legislation must only include proposals that directly change federal spending and not add to long-term deficits.

The Senate parliamentarian, Elizabeth MacDonough, makes such judgments. She ruled that the measure did not meet the requirements, according to Senator Chuck Schumer, the minority leader.