WASHINGTON — Gov. Rick Perry of Texas warned Thursday that militants from the Islamic State in Iraq and Syria and other terrorist groups may have already slipped across the Mexican border.

Mr. Perry said there is “no clear evidence” that terrorists have entered the United States illegally across the southern border. But he argued that illegal immigration should be considered a national security issue as well as a social and economic problem, and as evidence he cited the increase in violent crimes committed by illegal immigrants.

“I think there is the obvious, great concern that — because of the condition of the border from the standpoint of it not being secure and us not knowing who is penetrating across — that individuals from ISIS or other terrorist states could be,” he said during a conference on border security and immigration at the Heritage Foundation.

His speech came after Mr. Perry pleaded not guilty to two felony counts of abusing his power on Tuesday after being indicted by a grand jury last Friday, making him the first Texas governor to face criminal charges in nearly a century. Mr. Perry has called the charges a “farce,” and he is contemplating a second run for the Republican presidential nomination. He is scheduled to appear in New Hampshire this weekend.