"Certainly, emotionally, causes you to question what in the heck we are doing there. But on the other hand, we have to step back and look at what is in out nation's best interests," Corker said.
Karzai alleged that U.S. and coalition forces were colluding with Taliban leaders in Afghanistan, as a way to undercut Karzai's hold on power in the run up to the White House's 2014 withdrawal deadline.
Last month, the Afghan president ordered U.S. special operations units out of Wardak province, amid allegations of murder, torture and abuse of Afghan civilians at the hands of those forces.
A joint U.S.-Afghan inquiry into those allegations is still underway.
His comments last Sunday came shortly before meeting with new Defense Secretary Chuck Hagel, who was making his first trip to the country as DOD chief.
"At many levels, [it] was bizarre," Sen. Lindsey Graham (R-S.C.) said regarding Karzai's accusations of collusion between American and Taliban forces in Afghanistan.
"From the U.S. point of view, it was just offensive and . . . is wholly unwelcome by the American people," Graham added.
For his part, Sen. John McCain (R-Ariz.) McCain said Karzai's remark was "a regrettable statement" but in line with the Afghan president's attempt to position himself as a political player in postwar Afghanistan.
That said, the new Pentagon chief was not to blame for Karzai's outbursts, according to McCain.
"I do not put any responsibility on Chuck Hagel" for Karzai's comments and the tumultuous outcome of his first visit to the country, he said. "Chuck is in no way responsible for that."
The Arizona Republican also dismissed arguments that Karzai's outlandish comments indicated the U.S. no longer has a viable partner in Afghanistan and should pull out of the country ahead of schedule.
Some on Capitol Hill are concerned Karzai's recent statements and edicts restricting American operations in the run up to the 2014 withdrawal could place U.S. and allied forces at risk.
"I hope it is not used to shape out policy [in Afghanistan]," Corker said, noting he has had several conversations in previous meetings with Karzai "that were equally bizarre."
"The corruption that goes on with him there . . . all of the things [and] the way he deals with us, and the way he deals with the nation, does makes you" question his long-term goals for American and Afghan relations.
"He is a problem, but I think we have to look beyond that to decipher what is in our best interests," he added.
The kind of rhetoric coming out of Kabul in recent weeks reinforces the need for the White House to set up a long-term, postwar agreement with Afghanistan before the 2014 withdrawal, according to McCain.
"It means we need to either have a permanent [security] agreement post-2014 or make plans to leave" on schedule, McCain said.
"Right now, [Karzai] does not know, I do not know, nobody knows what the post-2014 [U.S] troop presence will be -- and that is what the Afghan people are most interested in," he added.
The Pentagon is considering stationing more than 13,000 American troops in Afghanistan after U.S. and allied commanders officially end combat operations in the county next year.
Marine Corps Gen. James Mattis, former Central Command chief, said he recommended to the Pentagon and White House that a postwar force of 13,600 U.S. soldiers, sailors, airmen and Marines remain in Afghanistan after the administration's 2014 withdrawal date.
The post-war NATO force in Afghanistan would likely be half of the total U.S. forces Mattis recommended to DOD leaders, the four-star general told Congress earlier this month.
Gen. John Allen, former head of all U.S. forces in Afghanistan, suggested as few as 6,000 U.S. soldiers, or as many a 10,000, could remain in country after 2014.
Graham agreed with McCain, noting Karzai's comments should not prompt a quicker U.S. withdrawal from Afghanistan, but added Washington could not take such allegations lying down.
"It is in our interest to get it right in Afghanistan, and when you have outrageous statements like this, you need to push back . . . and reject the construct" of the argument, which Defense Secretary Chuck Hagel and DOD leaders have done, Graham said.
The bigger threat, according to Graham, is what kind of effect Karzai's comments will have on local Afghan leaders, who remain wary of the central government in Kabul
With over a year to go before all U.S. combat troops are removed from the country, local and national leaders are doing all they can to solidify their power bases across Afghanistan.
That pressure could force Afghan leaders -- particularly at the provincial and district level -- to forge alliances with the Taliban rather than the central government, to fill the power vacuum left after the U.S. departure.
If that happens, the political impetus in Washington to support Afghanistan after 2014 will be virtually non-existent, according to Graham.
"I am not going to invest in a country where I see no hope," Graham added. "They have got to want this more than we do."
President Obama announced the administration would be pulling out half of the 66,000 American service personnel in Afghanistan by this spring.
The final 32,000 American forces remaining in Afghanistan after this spring's planned troop withdrawal will start coming home following the country's presidential election in April 2014 — officially ending America's combat role there that same month.