Attorney General Ken Cuccinelli II (R) said he might run for the U.S. Senate in 2014, possibly setting up a race against one of Virginia’s most popular politicians, Democrat Mark R. Warner.

Cuccinelli, who garnered national attention for suing the federal government over the new health-care law, had said he would run for reelection or governor in 2013. But in an interview with The Washington Post, he said for the first time that he could instead run for the Senate.

In the interview, he accused Warner — a former governor who has expressed frustrations with the workings of the Senate — of failing to lead and challenge authority.

“I understand from people he and I both talk to that he’s pretty frustrated with it,’’ Cuccinelli said Thursday. But, he added, “I don’t see him doing anything to change that system. He hasn’t even tried.”

Cuccinelli said that Warner should challenge his caucus — including Sens. Harry M. Reid (Nev.), Richard J. Durbin (Ill.) and Charles E. Schumer (N.Y.) — instead of voting alongside them.

“He has a really liberal caucus,” Cuccinelli said. “It wouldn’t be hard to articulate an alternative to Harry Reid in the Democrat caucus.”

Warner, who was elected to the Senate in 2008 with more votes than any politician in state history, has not said whether he plans to run for reelection. Some Virginians want him to run for governor again — or president.

“Once again, Mr. Cuccinelli is wrong on the facts but never in doubt,” Warner spokesman Kevin Hall said of Cuccinelli’s comments.

Political observers say that Cuccinelli is testing the waters of a Senate race early to scare off any other potential Republican candidates. Already, there’s a crowded GOP field, led by former governor and senator George Allen, hoping to next year replace retiring Sen. James Webb (D).

“He’s keeping his options open and discouraging others,” said Stephen J. Farnsworth, a political analyst at George Mason University. “He’s sending a message to a lot of other Republicans.”

Cuccinelli, easily elected as part of a GOP sweep in 2009, has quickly become a tea party favorite, suing the federal government over the health-care law, advising colleges that they could not adopt nondiscrimination policies protecting gays and subpoenaing documents involving a former climate scientist at the University of Virginia.

Farnsworth said that Cuccinelli, who has been outspoken in his views in Virginia and on national television, would easily win a nomination contest but could have a more difficult time in a general election, where successful Republicans often downplay their conservative credentials. “He’s shown a real unwillingness to move to the center,” he said.

A Post poll in May showed that 46 percent of respondents said they approved of how Cuccinelli was doing his job; 27 percent disapproved. The poll also showed that 61 percent of Virginians approved of the way Warner was handling his job; 24 percent disapproved.

Warner has spent months, largely behind the scenes, trying to broker a deficit-cutting plan alongside a group of bipartisan senators known as the “Gang of Six.” Although the plan gained momentum as part of the debt-ceiling debate last month, Congress passed a different bill signed into law by President Obama.

Cuccinelli said that Warner could have been successful with the “Gang of Six” plan had he been willing to battle his caucus.

When it came time to appoint members to a new “supercommittee” tasked with finding more than $1 trillion in budget cuts before Christmas, Reid — not a fan of the “Gang of Six” plan — did not appoint Warner.

Warner, known in Virginia for persuading Republican lawmakers to pass a budget that made record investments in core services by imposing higher taxes, had made no secret of wanting to be on the committee.

“Warner was given the back of Reid’s hand on this debt thing,” Cuccinelli said. “He was out there playing himself as leader, leader, leader, [and Reid said,] ‘Mark who?’ ”

Cuccinelli still expects to run for reelection, although he would consider running for the gubernatorial nomination against Lt. Gov. Bill Bolling (R) in 2013 or the Senate in 2014.

Cuccinelli said he hasn’t spoken to Bolling about his future. Bolling, he said, has never asked.

In spring 2008, Bolling surprised many in Virginia, including then-Attorney General Robert F. McDonnell, when he decided to run for reelection instead of running for governor. That allowed McDonnell and Bolling to run as a team. McDonnell is supporting Bolling for governor.

Bolling has said he expects Cuccinelli to run for reelection while he runs for governor. But on Tuesday, he said that Cuccinelli would make a formidable Senate candidate.

“A lot of the issues he is very passionate about are federal issues, making sure the federal government adheres to constitutional limitations,” Bolling said. “I can’t think of anyone who would be a stronger candidate than he might be, if that’s what he chooses to do.”