As New Mexico electors cast their votes this week, President Trump's campaign team filed a lawsuit over the state's use of ballot drop boxes.

The Land of Enchantment voted heavily in favor of former Vice President Joe Biden. According to Fox News' Decision Desk, the Democrat bested the Republican incumbent by almost 11 percentage points: 54.3% to 43.5%. New Mexico certified the vote on Nov. 24.

While the 2,097,000-person swing state has sided with Democrats in six of the past seven presidential elections, the Trump campaign and Republican supporters remain as unconvinced today of his loss as they were in November.

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The lawsuit filed in the U.S. District Court accused election regulators of violating state law regarding absentee ballot drop boxes, contending that they should be monitored by video surveillance -- under the same protective oversight as "secured containers" -- and that election workers were not following rules by allowing voters to deposit completed absentee ballots in drop boxes at voting locations. 

Five self-proclaimed GOP electors hold an unofficial ceremony to endorse the reelection of President Donald Trump, Monday, Dec. 14, 2020, in the lobby of the Capitol building in Santa Fe, N.M. The meeting took place as the official electors cast the state's five electoral votes for Joe Biden in a closed meeting upstairs. (AP Photo/Cedar Attanasio)

More than 40% of the 928,230 ballots cast in New Mexico were reported to be absentee ballots, according to USA Today.

While absentee and mail voting were critical components of a presidential election in a pandemic, the president has opposed such methods.

In October, the state's Republican Party sued over the drop boxes, accusing county clerks of incompetency and using boxes outside precinct boundaries. The party withdrew its complaint, however, after Secretary of State Maggie Toulouse Oliver reiterated guidance.

Nevertheless, Republicans have worked with the Trump campaign since then to invalidate the electoral vote -- also calling for a statewide canvass of absentee ballots.

In a press release, former Congressman Steve Pearce said Republicans "questioned these drop boxes and the entire election process."

As electors cast their votes, Republican electors in the Capitol Building signed unofficial papers marking their support for Trump and Vice President Mike Pence, according to The Associated Press

The president's legal fight has so far been largely unsuccessful, however, with more high-ranking Republicans recognizing Biden's victory this week.

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In October, a Trump-appointed federal judge in Pennsylvania dismissed a lawsuit from the administration to limit the number of drop boxes in the state for mail-in ballots. 

U.S. District Court Judge J. Nicholas Ranjan said that the GOP’s claims to harm were “speculative” and that "the job of an unelected federal judge isn't to suggest election improvements, especially when those improvements contradict the reasoned judgment of democratically elected officials."

In Texas, Democrats also shot down Republican Gov. Greg Abbott’s directive to limit ballot drop boxes to one per county. 

Fox News' Morgan Phillips and The Associated Press contributed to this report.