The Texas Department of Public Safety has been instructed to immediately increase its efforts to secure the Texas-Mexico border with a $1.3 million-per-week operation, the offices of Texas House Speaker Joe Straus, R-San Antonio, Lt. Gov. David Dewhurst and Gov. Rick Perry announced Wednesday evening.

The increased enforcement is in response to the recent surge of undocumented immigrants breaching the Texas-Mexico border, including more than 33,500 unaccompanied minors who have been apprehended in the U.S. Border Patrol's Rio Grande Valley sector since October.

"The U.S. Customs and Border Patrol … has apprehended more illegal immigrants in the Rio Grande Valley in the first eight months of the current federal fiscal year (over 160,000) than it did for all of fiscal year 2013 (154,453). In May 2014 alone, USCBP reported apprehending more than 1,100 illegal immigrants per day in the Rio Grande Valley," the state leaders said in a joint news release.

"This year, like last year, more than half of the individuals apprehended at the Texas-Mexico border by USCBP are from countries other than Mexico," they added. "Additionally, 34,000 unaccompanied alien children (UAC) have been apprehended in Texas so far this year, with estimates that number will reach 90,000 by the end of the fiscal year. By comparison, 28,352 [unaccompanied minors] were apprehended in fiscal year 2013."

The U.S. Border Patrol has said most of the migrants coming during the recent surge are from Central America.

The state leaders' announcement comes on the same day that U.S. Rep. Henry Cuellar, D-Laredo, and U.S. Sen. John Cornyn wrote U.S. Department of Homeland Security Secretary Jeh Johnson seeking answers about the safeguards in place to prevent the unaccompanied minors from ending up in the hands of sexual predators or other alleged criminals. By law, minors must be processed and released by U.S. Border Patrol and Immigration and Customs Enforcement within 72 hours and turned over to U.S. Health and Human Services authorities or guardians.

"Does DHS have any measures in places to track unaccompanied children after they are placed in the custody of HHS or a guardian designated by that Department?" they wrote. "If not, then how does your Department help ensure that they do not end up in the hands of predators or sex offenders? If the child does not show up for their immigration court proceedings, do DHS officials check up on them to make sure that they are safe?"

Details about when the state's new border security plan will begin or what it entails were not specified in the statements from the Republican leaders, and calls and emails to Texas DPS officials seeking comment were not immediately returned.

"With this letter, you are directed to plan and execute a surge operation of increased law enforcement in Texas border counties. You are authorized to utilize all existing appropriated funds toward this operation," Perry, Dewhurst and Straus said in a letter to DPS director Steve McCraw. "To the extent necessary, we will utilize our authority as governor and as co-chairs of the Legislative Budget Board to facilitate adjustments to the DPS budget until next session. The cost for this operation will need to be addressed by the next legislature in the supplemental appropriations bill."

The announcement comes after some lawmakers called for a special session of the Texas Legislature to provide monies to address the issue. A special session would not be required however, if DPS uses funds already appropriated for the agency.

This week, Dewhurst called for a repeat of a recent operation called "Operation Strong Safety," which added more state-based security in the Rio Grande Valley.

In the letter sent to McCraw, Perry, Dewhurst and Straus indicated an expanded version of the operation should be considered by the DPS.

"The results achieved through this operation need to be continued and implemented over a wider area. Clearly, committing more of your resources will not end the humanitarian issues on the border, nor is it a complete solution to what is ultimately a federal responsibility," they wrote. "But the professional law enforcement resources at the Texas Department of Public Safety can reduce crime, ensure the safety of Texas citizens and support the strained resources of local law enforcement and the U.S. Customs and Border Protection."

Straus, the only member of the leadership team who will return to Austin next legislative session, addressed potential cost concerns in a letter to state representatives.

"I also want to be clear that this approach is not simply writing a blank check to DPS," he wrote. "We will closely monitor and evaluate the costs and results of this effort. In my conversations with Director McCraw, I have made it clear that I would support his assessment and recommendations, while remaining prudent with taxpayer dollars. That is why I am directing the House Committees on Appropriations and Homeland Security and Public Safety to monitor and assess the cost and outcomes of this operation between now and next January."

Texas Attorney General Greg Abbott, the Republican candidate for governor, praised the decision. Abbott wrote Johnson, the secretary of DHS, last week requesting $30 million in emergency funding for state-based border operations.

"The Department of Public Safety will have the tools and resources it needs to curtail illegal smuggling, horrific human trafficking and cartel imported crime," he said in a statement on Wednesday. "Securing the border will reduce the illegal activity which – in turn – will promote the legitimate trade that helps make Texas the leading exporting state in the country."

The move is likely to draw opposition from Democrats, specifically border representatives, who have said that more "boots on the ground" will not address the key causes of the migration.

"What is needed are not more "boots on the ground" or any other euphemisms for the militarization that both impacts border residents' daily lives and is inadequate to deal with the specific issue at hand," state Sen. José Rodriguez, D-El Paso, said in a statement last week in response to Abbott's request.

State Sen. Leticia Van de Putte added: "Washington must tackle the root causes of this crisis: weak governments, entrenched poverty and the growing power of violent criminal actors in Central America. Texans have a long tradition of looking after our neighbors in times of need. These too are children of God. State and federal government should follow suit, and partner with our faith-based organizations, nonprofits, food banks, and health providers to help these children."

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