U.S. and Afghan officials reportedly have reached a tentative agreement on a critical security pact -- which would include President Obama writing a letter to the Afghan people acknowledging mistakes during the "war on terror."

According to Reuters, an Afghan spokesman said Tuesday that Obama agreed to write the letter, to be presented with the draft security pact at a meeting of tribal elders later this week.

The New York Times, citing a spokesman for Afghan President Hamid Karzai, reported that Secretary of State John Kerry proposed the letter in a conversation with Karzai.

Karzai asked that Obama sign it, and Kerry reportedly agreed. The letter apparently helped them reach a tentative deal authorizing U.S. raids on Afghan homes in certain circumstances, which had been an area of disagreement.

White House Press Secretary Jay Carney, at Tuesday's daily press briefing in Washington, would not confirm or deny the letter when asked by Fox News.

"We don't comment on presidential correspondence," he said.

He added: "We take every precaution to prevent civilian casualties and we always express regret when civilians are killed."

However, a senior State Department official tells Fox News Kerry has told Karzai he is considering his request for a letter from the administration.

Carney also would not confirm that any overall draft deal was in place.

"There are ongoing conversations," he said, noting that Kerry and Karzai had talked.

The meeting of the Loya Jirga, a traditional council of 3,000 prominent Afghans, can revise or reject any clause of the draft agreement.

The negotiations have been marked by a series of disagreements. One contentious provision says U.S. forces staying in Afghanistan beyond 2014 cannot be tried in local courts for any crimes they commit. But that could be a deal-breaker for tribal leaders, clerics and other influential figures who gather Thursday to debate the draft agreement.

The Loya Jirga's members may seek amendments, but if they reject the security pact, it is almost certain the Afghan government won't sign it. Even if it is approved, the final decision will be made by Parliament.

Divisions run deep in Afghanistan over conceding the right to prosecute U.S. soldiers for crimes committed in the country.

In eastern Afghanistan, scores of university students wearing headbands bearing an inscription from the Koran burned an effigy Tuesday of Obama to protest the pact and its provision relinquishing prosecution of American soldiers in an Afghan court. A protest meeting also was held Monday in the Afghan capital of Kabul.

Afghans are still angry over several incidents involving international troops, including the 2012 accidental burning of hundreds of copies of the Koran; a shooting spree that year by a U.S. soldier in southern Afghanistan that killed 16 people, mostly women and children; and the unintentional deaths of civilians by wayward bombs.

U.S. congressional aides originally told The Associated Press that the accord also explicitly denied U.S. soldiers the right to enter Afghan homes, something Karzai has demanded. But a senior U.S. official said Tuesday in Washington both sides were still negotiating the point, with the U.S. seeking more flexibility. The official said the key is to agree on acceptable phrasing that provides more flexibility, but so far the sides have reached no agreement.

According to the Times, the letter from Obama was meant to help resolve that issue.

If the pact is passed, U.S. troops will have sole control over Bagram Air Field, north of Kabul, but will share facilities on eight Afghan-run bases throughout the country, Pashtun said.

The Associated Press contributed to this report.