Perry, dressed in a tan suit and cowboy boots, handed the letter to Obama adviser Valerie Jarrett after greeting Obama at the airport in Austin. Obama is in Texas for fundraisers and a speech to students at the University of Texas.
Perry, a Republican, clapped when Obama descended from Air Force One and then shook hands with the Democratic president.
In his letter, Perry said there was "mounting evidence of spillover violence" from Mexico and asked Obama to send more resources to the region to "step up and finally do what is needed to secure our borders."
"Absent stronger federal action, it's only a matter of time before violence affects more innocent Americans," Perry's letter said. "We cannot afford to allow these (Mexican drug) cartels to believe they're free to extend their reach across the border onto American soil."
The letter cites several examples of violence on the Texas side of the border, including an unexploded grenade that rolled into a bar in Pharr in 2009, a weapon later connected to a similar attacks in Monterrey, Mexico; the assassination of a member of the Juarez cartel living in El Paso, and the recent bullets fired in Ciudad Juarez, Mexico, that landed in the walls of El Paso city hall. Unlike in Mexico, no innocent civilians have been killed or injured by drug-gang violence in Texas.
Calling the pending deployment of 286 National Guard personnel "clearly insufficient," Perry asked Obama to "quickly deploy" 1,000 troops and technology to the Texas-Mexico border.
"We must show the cartels that Washington will no longer tolerate their terrorizing and criminalizing the border region," Perry's letter said.
White House spokesman Bill Burton, speaking to reporters before Perry handed the letter to Jarrett, said, "the president has put more assets on the border to secure the border than has ever previously been there. That includes National Guard troops, technology, things he has done on enforcement. That's something that he is working very hard on."
Perry has been at odds with Washington over what he sees as the federal government's intrusion into state affairs, but he has consistently said that securing the border was a federal responsibility.
Perry, speaking at a conservative think tank after he greeted Obama said he would have preferred a "more in-depth exchange of ideas" with the president, and expressed his hope that "he'll take the time to read it."
Perry also noted that his appearance at Obama's arrival in Austin was "an appropriate and gracious thing."