Experts argue there are two claims under international law that might justify an operation inside Pakistan by the Afghan National Army. One is a country's "right of hot pursuit." Another justification is a country's right to self-defense.
Last week, Karzai insisted that his country has the right to chase Taliban fighters who flee into Pakistan's tribal regions after they carry out attacks in Afghanistan.
"Afghanistan has the right of self-defense. When [insurgents] cross the territory from Pakistan to come and kill Afghans and to kill coalition troops, it exactly gives us the right to go back and do the same," Karzai said.
Karzai said Afghan forces would kill specific Taliban leaders in Pakistan's tribal regions who are accused of planning and organizing cross-border attacks into Afghanistan.
Islamabad has condemned Karzai's remarks as "irresponsible," saying any incursion by Afghan forces would violate Pakistan's sovereignty and territorial integrity.
Pakistani Foreign Minister Shah Mehmood Qureshi described Karzai's threat as "illegal" under international law, saying the only way to combat extremism in the border region is by noninterference in each others' internal affairs.
In Kabul, political analysts like Rashid Waziri are arguing that Afghanistan does have a legal right to attack and kill militants in the tribal regions if Pakistan fails to stop them.
"We have the right to strike our enemies inside Pakistan or its tribal territories. The Turkish government gave itself the right to bomb and target Kurdish rebels in northern Iraq and to eliminate their bases. So this is an international right. And everybody can benefit from it," Waziri said.
But Jim Denselow, an expert on defense issues at Kings College London, says there is no valid legal comparison between the Afghan-Pakistan crisis and Turkish incursions into northern Iraq.
"The key difference is that Turkey is justifying its actions in northern Iraq along the lines of previous agreements it had with Saddam Hussein's regime. [Those agreements were] in terms of the 'right of hot pursuit' of Kurdish rebels into Iraqi territory -- which, of course, hasn't been sovereign Iraqi territory since 1991 when the no-fly zones were created and the autonomous entity, which is the Kurdish Regional Government, was essentially born," Denselow said.
"So that's a very specific case. A very unique case of a bilateral agreement between two countries, one of which wasn't even totally sovereign. And, of course, [there is] the fact that Turkey is an incredibly strong power vis-a-vis a weakening Iraqi one."
In addition to Turkey, the right to "hot pursuit" has been raised by Colombia to justify air strikes against FARC rebels fleeing into neighboring Ecuador. Israel has used the same argument to justify military incursions into the Gaza Strip. And in 2000, the Democratic Republic of the Congo and Uganda approached the International Court of Justice over the issue when the Ugandan Army claimed the right of "hot pursuit" for its forces to go after militants in Congo.
Law Of 'Hot Pursuit'
Nick Grono, the deputy president of operations for the International Crisis Group, agrees that those cases differ from Afghanistan's situation and that the doctrine of "hot pursuit" probably isn't applicable for Afghan incursions into Pakistan.
Grono notes that "hot pursuit" is a concept under international law that originated out of the laws of the sea.
On land, he tells RFE/RL, the right to "hot pursuit" has evolved and been recognized under international law as the chasing of armed aggressors across international borders.
"I don't think this is a case of 'hot pursuit' that we are talking about [in Pakistan's tribal regions]. Historically, [it] means you are pursuing a fugitive. The doctrine of hot pursuit comes from the law of the sea. And it used to be chasing a fleeing ship, for instance, or chasing someone who retreated into another country," Grono said.
"The conditions applying to hot pursuit are pretty restrictive. That doesn't appear to be what Karzai was talking about. He was talking not so much about pursuing someone as going across the border to hit Taliban leaders who are enjoying safe haven in Pakistan. I suspect that what he was looking at was more a case of preemptive self-defense."
International law on a country's right to self-defense stems from Article 51 of the UN Charter and decisions made by the International Court of Justice.
"There is a provision under international law for self defense," Grono said. "The way it works under international law is that there is a right of preventive self-defense if there is a very immediate threat -- and it is an overwhelming threat -- and if the only possible response is to strike first."
Legal scholars in the U.S. military have had studies published by the U.S. Defense Department which explore the legalities of antiterrorism operations under both the doctrines of "hot pursuit" and self-defense.
Those studies note that other legal justifications for the use of cross-border military force include invitation, peace-time reprisals, protection of a country's own citizens, and humanitarian intervention.
Ultimately, military incursions must be consistent with international law -- as defined by the International Court of Justice. Otherwise, as one study published in 1989 by the U.S. Department of Defense concludes, "those acting to preserve the rule of law in the face of terrorist threats will become indistinguishable from the evils" they seek to prevent.