(CNN) A possible government plan to send migrants who are in federal custody to South Florida sparked concern from local officials this week, and one mayor offered a proposal of his own.

"Bring them to the Trump hotels and ask the President to open his heart and home as well," Broward County Mayor Mark Bogen said.

Bogen said in a statement that he and other local officials learned this week from US Customs and Border Protection of a plan to release hundreds of migrants weekly into the area.

"This is a humanitarian crisis. We will do everything possible to help these people," Bogen said. "If the President will not provide us with financial assistance to house and feed these people, he will be creating a homeless encampment."

Neighboring Palm Beach County -- home to Trump's Mar-a-Lago resort -- also received a similar notification from CBP, officials there said.

The sheriff said the agency had recently informed the county of a plan to transport 135 migrants from El Paso, Texas, to Broward and Palm Beach counties twice a week.

"The President wants to send his problems to Palm Beach County. And that's not fair," Palm Beach County Mayor Mack Bernard told CNN on Friday.

CBP: 'We are not flying anyone to Florida'

Acting CBP Commissioner John Sanders said in a statement Saturday that the agency "has no plans" to transport migrants to northern or coastal cities, including those in Florida.

The agency is, however, transporting people to less crowded facilities along the Southwest, he said in the statement, calling it "the latest contingency we've exercised in response to the ongoing humanitarian and border security crisis, which has overwhelmed the entire immigration system."

Saturday's statement reaffirms CBP's earlier statements on the matter.

On Friday, a CBP official said there were no plans to send migrants to Florida "immediately," adding that the agency has been in "preliminary" conversations with a number of localities across the country about "contingency plans" to move groups of recently apprehended immigrant families.

"We are not flying anyone to Florida. We were in preliminary planning stages across the nation ... for having contingency plans because we are overcapacity and for our safety and the safety of those that we are charged with caring for, we can't keep them in these facilities," the CBP official said of intake facilities along the US-Mexico border.

"This is an emergency of 'get them out of our facilities as quickly as we can and as safely as we can.' This is an emergency. The entire system is overwhelmed."

The official said record number of family units and unaccompanied minors crossing the border has created "a serious backlog" at intake facilities and forced immigration authorities to move the migrants to other areas for processing before release.

CBP last week began moving immigrants by bus and plane to other border communities along the US-Mexico border "to leverage available capacity for processing and holding," CBP said.

Since May 10, CBP has been busing families from the Rio Grande Valley to Laredo, Texas, the official said, as well as flying migrants on planes contracted from Immigrations and Customs Enforcement to Del Rio, Texas, and San Diego.

Everyone that is being moved by bus or plane is part of a family unit, and has been initially processed for criminal connections, and given a medical assessment to make sure they are medically cleared to fly, according to the official.

The CBP official said authorities were looking at locations across the country where CBP has temporary detention facilities and adequate computer systems to be able to process the immigrants upon arrival. Those locations are primarily along the northern and coastal border, the official said.

The official denied that the contingency plans being laid were targeting sanctuary cities, which would be in line with President Trump's stated intention of sending immigrants to sanctuary cities.

"All we are looking at right now is where we have the capacity and the bandwidth for the computer systems, and the computer systems to be able to do the processing," the official said.

Lawmakers trade blame

Several lawmakers who represent Florida in Congress said details were in short supply -- though they traded blame over who was responsible for the situation.

Republican Sen. Marco Rubio said he'd sent a list of questions over the matter to Acting Homeland Security Secretary Kevin McAleenan.

I sent a letter to the acting Secretary of @DHSgov regarding the plan to transport 500 unlawful migrants per month to both #PalmBeach & #Broward county #Florida



Customs & Border Protection is being overwhelmed by an unprecedented flow of asylum seekers on our border #Sayfie pic.twitter.com/1dZBUE32XU — Marco Rubio (@marcorubio) May 16, 2019

Republican Sen. Rick Scott's office said Democrats were to blame for refusing to fix a crisis at the border, adding that Scott is seeking additional information from local sheriffs, the White House and the Department of Homeland Security.

Democratic Rep. Ted Deutch slammed what he said was a "stunning amount of confusion" over the administration's immigration policy.

"Our diverse community treats immigrants with dignity and respect; the Administration should do the same," he said in a statement. "That starts with a thoughtful plan rather than a rash decision apparently made by some in the Administration without any consultation with the rest of the government."

Earlier this month, CBP said more people had been apprehended illegally crossing the US-Mexico border this fiscal year than any year since 2009. The CBP official said on Friday that the agency has apprehended on average of 4,500 people over the past seven days.

Sanctuary cities under fire

Word of the proposed plan to send large groups of migrants to South Florida comes weeks after Trump vowed to send migrants to sanctuary cities, local jurisdictions that limit cooperation with federal authorities when it comes to immigration enforcement.

The administration initially denied that the plan was under active consideration. After reports surfaced in the press where DHS officials said the plan had been scrapped, the President tweeted saying he was considering it.

"We're sending many many of them to sanctuary cities," Trump told a rally in Green Bay, Wisconsin, last month . "They ain't too happy about it. I'm proud to tell you that was actually my sick idea."

There are no sanctuary cities in Florida. And state lawmakers approved a sanctuary city ban earlier this month.

Bernard, a Democrat and Palm Beach County's mayor, told CNN Friday that he hoped reasons for transporting the migrants aren't political.

"We hope that this is not politically motivated," he said, "because of the fact that when we're dealing with issues in Palm Beach County in terms of homelessness, housing, hurricanes, we don't look at political affiliations. We look at addressing the needs of our residents."

Bernard said he hopes the administration will create a more concrete plan to deal with the situation. And local taxpayers, he said, shouldn't have to pick up the tab.