LOS ANGELES—On a day when another bus of migrants from Texas arrived in Los Angeles, the City Council approved a motion on Aug. 30 asking the City Attorney’s Office to investigate whether Texas Gov. Greg Abbott committed any crimes when he sent 42 migrants on a 23-hour bus ride to downtown Los Angeles in June.

The motion requests the office to begin proceedings on any potential legal action that could be taken against the state of Texas, Mr. Abbott, or any other entity involved in the planning and action of busing migrants to Union Station, where they arrived on June 14.

The council voted 13–0 to approve the motion, which was introduced by council members Eunisses Hernandez, Nithya Raman, Monica Rodriguez, and Hugo Soto-Martínez on June 16.

Ms. Hernandez and Councilman Curren Price were absent during the vote.

Texas has sent 11 buses of migrants to Los Angeles, beginning with the June 14 arrival, containing a total of 435 migrants.

The latest bus arrived Wednesday and contained 35 asylum seekers from Guatemala, Honduras, Peru, Russia, and Venezuela, according to the Coalition for Humane Immigrant Rights.

Mr. Abbott and Florida Gov. Ron DeSantis, who has sent similar shipments of migrants to New York, have defended their decisions, saying their states are overwhelmed by an influx of immigrants entering the country illegally, with Abbott citing the council’s recent decision to declare Los Angeles a “Sanctuary City.”

“The competition between these Republican governors about who could be more racist, I think, is just an utter failure and shows clearly that they do not have any intention to govern effectively,” Mr. Soto-Martínez said prior to Wednesday’s vote.

Mr. Soto-Martínez noted that a couple weeks ago, as Los Angeles was preparing for the arrival of Tropical Storm Hilary, Mr. Abbott “knowingly” sent a bus containing migrants, some of whom were children, to Los Angeles.

“Now how heartless do you have to be to send toddlers and small children knowing that everything that the city was preparing for an unprecedented state of emergency,” Mr. Soto-Martínez said. “The callous and disregard for lives of these families deserves their full investigation and accountability into the criminal actions of wrongdoing of Gov. Greg Abbott.”

Mr. Abbott’s office did not immediately respond to a request from City News Service for a comment on Wednesday’s council action.

The council also approved a resolution—in a 13–0 vote—calling upon Los Angeles County District Attorney George Gascón, state Attorney General Rob Bonta, and U.S. Attorney General Merrick Garland to investigate and report on the same issue.

The resolution also calls upon county, state, and federal government to “support the housing, placement, and necessary resources to ensure a dignified welcome to Los Angeles for the migrants.”

“Texas’ small border towns remain overwhelmed and overrun by the thousands of people illegally crossing into Texas from Mexico because of President Biden’s refusal to secure the border,” Mr. Abbott said in a statement after the first bus arrived in Los Angeles in June.

“Los Angeles is a major city that migrants seek to go to, particularly now that its city leaders approved its self-declared sanctuary city status. Our border communities are on the front lines of President Biden’s border crisis, and Texas will continue providing this much-needed relief until he steps up to do his job and secure the border,” he added.

The City Council approved a motion on June 9 seeking to formally establish Los Angeles as a sanctuary city.

Councilman Kevin de León said Mr. Abbott has “no incentive at all whatsoever to stop doing what he’s actually doing.” He said Los Angeles has and will accept immigrants and take care of them.

Mr. de León added that the problem has been exacerbated by what he termed the failure of leaders in Washington D.C.

“We’re going on almost four decades without any type of immigration reform,” Mr. de León said.

Councilwoman Imelda Padilla condemned Mr. Abbott’s move, calling it an “ugly form of political theater.”

“It’s against our dignity, in the humanity of all people, especially toward immigrants, families, and children who have fled their country due to injustices or threats against their lives, who have faced unimaginable obstacles to seek asylum,” Ms. Padilla said.

On Wednesday afternoon, Ms. Bass told KNX that if Mr. Abbott’s concerns and actions were legitimate and sincere then “someone in the government and Texas would notify us and coordinate with us.”

Ms. Bass said that’s not what’s happening.

“We hear about the buses headed our way when they’re on the way. We have no idea who’s going to be on the bus, how many people it is or what condition they’re going to be in when they get here,” Ms.Bass said. “Sometimes they haven’t had any food, barely had enough water.”