Republicans took the first step on Monday toward changing the Senate’s rules to speed the confirmations of Trump administration nominees being slowed by Democratic opposition, touching off the latest in a yearslong tit for tat between the two parties that has weakened the filibuster.

The move is a response to Democrats’ refusal to allow President Trump’s nominees to be considered, which has slowed their confirmations and frustrated the president. But its consequences will reach beyond Mr. Trump’s tenure, effectively whittling down the ability of the minority to register any opposition to executive branch nominees below the cabinet level.

Senator John Thune of South Dakota, the majority leader, made the first move on Monday by introducing a resolution that would group 48 of Mr. Trump’s nominees together to allow them to be considered and voted on as a group. That will queue up a complex series of floor votes this week and next that, if successful, would create new Senate precedents meant to help Republicans clear a growing backlog of nominees.

Republicans, who hold 53 seats, will try to muscle through the rules change using a simple majority, a tactic known as “going nuclear,” in part because of the charged partisan cloud it can leave over an institution that once prided itself on operating according to consensus.

It is the latest change to chip away at longstanding Senate precedent in the face of an increasingly polarized political environment.

Speaking on the Senate floor, Mr. Thune framed the rules change as a necessary response to what he framed as an unprecedented Democratic blockade against fast confirmation of any of Mr. Trump’s nominees, including lower-level picks that have traditionally been confirmed by voice votes or by unanimous consent.