MEXICO CITY, June 10 (Reuters) - Mexican President-elect

Claudia Sheinbaum said on Monday she would put up for discussion

proposed constitutional reforms, including a judicial overhaul

that has spooked markets, before the next congressional session

kicks off.

The judicial reform would replace an appointed Supreme Court

with popularly elected judges, as well as for some lower courts,

which critics allege would fundamentally alter the balance of

power in Mexico.

Sheinbaum, speaking in a press conference following a

meeting with outgoing President Andres Manuel Lopez Obrador,

said the reform would be "among the first" that could be passed,

along with some boosted social benefits.

She added she did not believe the proposed reforms would

impact the peso, which tumbled following her election win

earlier this month.

As Sheinbaum was speaking, however, the peso weakened by

nearly 2% against the U.S. dollar in international trading.

Some of the measures are part of a slew of

constitutional reforms Lopez Obrador proposed in February that

would also eliminate key regulatory agencies.

At the time they did not cause market jitters, but investors

sounded the alarm as the ruling coalition honed in on a

congressional super-majority needed to pass constitutional

reforms in the June 2 election.

The coalition led by MORENA secured a two-thirds

super-majority in the lower house but fell just short in the

Senate, although analysts believe those extra votes can likely

be secured through negotiation.

While the newly elected Congress will take office at the

beginning of September, Sheinbaum will not be inaugurated until

a month later, which could give Lopez Obrador and lawmakers a

window to try to enact the reforms.

"In the case of the judicial reform, (discussion) should

be through the bar association, professors of law, the ministers

and magistrates themselves," Sheinbaum said.

She added she would name her cabinet next week, and that she

would receive a team sent by U.S. President Joe Biden on

Tuesday.

Lopez Obrador had said earlier in the day he would not

pressure Sheinbaum to rush the package of constitutional reforms

through Congress.

Mexico's peso is now down 8% since the elections Sheinbaum

and her party won in a landslide - its biggest plunge since the

COVID-19 pandemic - while the country's main stock index has

fallen nearly 4%.

(Reporting by Raul Cortes Fernandez, Ana Isabel Martinez, Kylie

Madry, Diego Ore, Lizbeth Diaz and Aida Pelaez-Fernandez;

Editing by Brendan O'Boyle, Alistair Bell, Christian Plumb and

Lincoln Feast.)