MEXICO CITY (Reuters) -Mexico's president on Thursday vigorously backed his party's selection of former Mexico City Mayor Claudia Sheinbaum as its candidate to succeed him in 2024, dismissing objections about the process by her main rival, who threatened to quit the party.

The ruling National Regeneration Movement (MORENA) declared Sheinbaum the winning candidate a few hours after her closest competitor, ex-foreign minister Marcelo Ebrard, said the primary contest had been irredeemably tainted by irregularities.

President Andres Manuel Lopez Obrador, speaking at a regular morning press conference extended a hand to Ebrard, calling him a "very good person," a good leader and his friend, as he urged him to remain united with the leftist MORENA.

But he rejected Ebrard's demand that the polls to pick a candidate be redone, and fell in behind the winner.

"I support Claudia Sheinbaum," Lopez Obrador said, calling the process of surveying some 12,500 people in which she beat out five other rivals historic and unprecedented.

"I don't see any problem."

Under Mexican law, presidents can only serve a single six-year term.

Victory would make Sheinbaum Mexico's first woman leader.

Ebrard says he will decide his next move on Monday and has left open the possibility of running with the center-left Citizens' Movement (MC), the only significant opposition party yet to back a candidate for the June 2 presidential election.

On Thursday, the 63-year-old Ebrard indicated his time in Lopez Obrador's party was nearing an end.

"What is clear to us is that there's no longer space for us inside MORENA," he told Mexican radio.

Ebrard has been allied with Lopez Obrador for more than two decades, and succeeded him as mayor of the capital in 2006.

If he decides to run against MORENA, Ebrard, who is popular with many middle class voters, could cause problems for both Sheinbaum and her main opposition rival, Xochitl Galvez, a charismatic and unconventional senator of Indigenous origin.

Still, recent polling suggests he could face a huge challenge mustering enough votes to win with MC.

An Aug. 30 to Sept. 3 voter survey by polling firm Parametria showed MC garnering 4% support for the presidency in a generic question that did not name any candidates.

MORENA and its allies were seen winning 60% or more.

During the press conference, Lopez Obrador speculated Ebrard could run for the presidency as an independent candidate.

A campaign source for Ebrard said he had no current plans to run as an independent.

(Reporting by Dave Graham; Additional reporting by Raul Cortes and Ana Isabel Martinez; Editing by Stephen Eisenhammer, Mark Porter and Jamie Freed)