The three leading senators pursuing the Republican presidential nomination — Ted Cruz (Tex.), Rand Paul (Ky.) and Marco Rubio (Fla.) — have clashed recently on foreign policy and other issues, but they agree on this: Congress needs to wield its constitutional muscle inside the District of Columbia.

Paul on Thursday announced his plans to introduce the “Defend Our Capital Act,” which would end most of D.C.’s strict local gun laws, becoming the last of the three senators to introduce bills this Congress overturning policies implemented by the District’s locally elected officials.

Rubio introduced his “Second Amendment Enforcement Act” in March. Like Paul’s bill, it would eliminate local gun laws, including a gun registration requirement and a ban on assault-type weapons, and pave the way for recognition of out-of-state concealed-carry permits. That same month, Cruz led an effort to overturn one D.C. law that sought to protect employees from employer retaliation over reproductive health decisions and another that prevents religious colleges from banning gay student groups.

The fourth Senate Republican seeking the presidency, Lindsey Graham of South Carolina, has not introduced a bill this Congress targeting D.C., but he cosponsored a 2007 bill that would have much the same effect as Paul’s new bill.

Why do these men seeking the highest office in the land find it worthwhile to spend time attacking laws passed by local officials elected by D.C.’s 660,000 residents? Because they can: Article I, Section 8 of the Constitution gives Congress the power to “exercise exclusive Legislation in all Cases whatsoever” over the capital.

And while Congress delegated most of that responsibility to the Home Rule government in the early 1970s, federal lawmakers frequently butt in for their own political reasons — whether, in Paul and Rubio’s case, to bolster their standing with gun-rights advocates, or, with Cruz, to burnish their bona fides for religious conservatives. And targeting D.C., which does not have a voting representative in Congress, comes at a lower political cost than proposing legislation that might have a national impact.

Del. Eleanor Holmes Norton (D), the District’s nonvoting member of Congress, said Paul’s bill is particularly “disappointing” because the libertarian-minded senator had previously voiced support for the District’s ability to legalize the possession of small amounts of marijuana. And, she said, the bill’s timing is “beyond irresponsible.”

“This one really gets on my nerves, because it comes at a time when there’s been a spike in gun crimes here and across the country … and it occurs after there’s been a specific threat on the capital of the United States,” she said, referring to an Islamic State terror threat.

“It’s an obvious ploy to get some attention to his flagging presidential campaign,” she added.

Paul polled at 3 percent in the most recent Washington Post/ABC News survey of likely Republican primary voters.