Weeks after sending President Obama a letter asking him to meet and discuss the illegal immigration influx in Texas, Gov. Rick Perry received his own invitation asking for the same.

In a letter on Monday, U.S. Rep. Joaquin Castro, D-San Antonio, asked Perry to meet with the entire Texas congressional delegation to talk about the border and to “help set a more positive tone.”

The invitation is the latest salvo in a tense back-and-forth between Castro and Perry that escalated after the governor’s decision to send up to 1,000 National Guard troops to the Rio Grande Valley to assist law enforcement in border-security operations.

“I invite you to meet with the entire Texas congressional delegation (which you have not done in several years), at your earliest convenience, to work together to get Congress to pass the supplemental funding necessary to stem the flow of minors making the dangerous trek while treating humanely the tens of thousands of children who have arrived in our great state,” Castro wrote.

Perry’s office could not be immediately reached for a comment.

The invitation, which a Castro aide said is open-ended and would accommodate Perry’s schedule, is as much a push for Perry to meet with Texas lawmakers as it is a response to his accusation that Castro misunderstood the governor’s intent when he decided to deploy the National Guard.

In a letter on Wednesday, Perry accused Castro of misunderstanding “the very positive role the Guard will play in tackling the border security crisis,” the Houston Chronicle reported. Castro had called Perry's decision “militarization” that would send the wrong message to children at the border.

Castro said in his invitation that he was disappointed the governor chose to visit the border and “pose by mounted machine guns as if on a trophy hunt.”

Should Perry accept, the clock is ticking on a meeting. In Washington, lawmakers have less than a week before adjourning for their August recess. At least one lawmaker has said that adjourning for more than a month without passing legislation concerning the border crisis could send a bad message to smugglers, and that without more funding, Immigrations and Customs Enforcement and the Customs and Border Protection would run out of resources later this summer.

Castro’s invitation comes days after his Republican colleagues from Texas sent a letter to Obama urging him to enforce immigration laws and to “stop the surge of illegal entries.” Every Republican from Texas — 24 representatives and two senators — endorsed the letter, which asked the president to suspend his deferred action policy and stop “catch-and-release” policies that give “convicted criminal immigrants and illegal immigrants a free pass.”