Citing interviews with two U.S. generals in a Senate Foreign Relations Committee report to be released this week, the Times said the strategy is aimed at disrupting the flow of drug money used to finance Taliban insurgents.
The addition of drug lords on the "joint integrated prioritized target list" reflects a major shift in counternarcotics strategy and means the traffickers will be given the same target status as militant leaders.
"We have a list of 367 'kill or capture' targets, including 50 nexus targets who link drugs and the insurgency," a general reportedly told the committee staff, the Times said.
On Sunday, President Barack Obama's national security adviser did not rule out adding more U.S. forces in Afghanistan to help turn around a war that he said is not now in crisis.
The administration is redefining how it will measure progress, with new benchmarks that reflect a redrawn strategy. An outline is expected next month.
Making the rounds of the Sunday talk shows, Jones did little to dispel the growing expectation that Obama soon will be asked to supplement the 21,000 additional forces he already approved for Afghanistan this year.
"We won't rule anything out," but the new strategy is too fresh for a full evaluation, Jones said. "If things come up where we need to adjust one way or the other, and it involves troops or it involves more incentives ... for economic development or better assistance to help the Afghan government function, we'll do that."
The Obama plan is supposed to combine a more vigorous military campaign against the Taliban with a commitment to protect Afghan civilians and starve the insurgents of sanctuary and popular support. It envisions a large development effort led by civilians, which has not fully happened, and a rapid expansion of the Afghan armed forces to eventually take over responsibility for security.
"If we can get that done ... we will know that fairly quickly," Jones said.
The system to measure progress in Afghanistan is several weeks from completion. It reflects creeping congressional skepticism about the war and its costs. The United States has spent more than $220 billion since the U.S.-led invasion of 2001, plus billions for more toward aid and development projects. By the United States' own admission, much of the aid money was wasted.
Members of the House Appropriations Committee wrote recently that they are worried about "the prospects for an open-ended U.S. commitment to bring stability to a country that has a decades-long history of successfully rebuffing foreign military intervention and attempts to influence internal politics."
The chairman of the Senate Armed Services Committee said Sunday he does not know how Congress would react to a new request for additional troops.
"It depends on what the facts and the arguments are," said Sen. Carl Levin, D-Mich. "It depends what our commanders in the field say. It depends also I think in part what our NATO allies are willing to do."
"My message to my Democratic colleagues is that we made mistakes in Iraq. Let's not 'Rumsfeld' Afghanistan," Graham said, referring to former Defense Secretary Donald H. Rumsfeld. Rumsfeld resisted sending a very large U.S. force at the outset of the Iraq war in 2003.
"Let's don't do this thing on the cheap," Graham said. He said he will "be shocked if more troops are not requested by our commanders."
Violence has spiked this year, with roadside bombs the militants' weapon of choice. There are relatively few direct firefights. There are signs the Taliban is pursuing a classic tactic of a smaller, weaker enemy waiting out a larger, militarily superior one.
Deaths among U.S. and other NATO troops have soared. With 74 foreign troops killed -- including 43 Americans -- July was the deadliest month for international forces since the start of the war in 2001.
There are currently 62,000 U.S. troops and 39,000 allied forced in Afghanistan, on top of about 175,000 Afghan soldiers and police. Some NATO countries plan to withdraw their troops in the next couple of years, even as the U.S. ramps up its presence.
The newly installed top U.S. general in Afghanistan is preparing an interim assessment that is expected to be a sober accounting of the difficulties of fighting an entrenched and technically capable insurgency eight years into the war. Gen. Stanley McChrystal is expected to identify shortfalls that should be filled by more forces -- perhaps a mix of Afghan, NATO and U.S.
His report had been expected this week but is now delayed at least until after the Afghan national elections on Aug. 20.
U.S. officials have said they are neutral on the election's outcome so long as voting comes off smoothly and with a minimum of irregularities. Jones cited the elections as evidence of progress.
He rejected the idea that a secret, hastily arranged gathering of the top U.S. defense officials in Europe last weekend carried a whiff of desperation.
"No, I don't think we're at a crisis level ... or that there's going to be any movement on the ground by the Taliban that's going to overthrow the government. We're going to have, I think, a good election," Jones said.
Jones appeared on "FOX News Sunday," NBC's "Meet the Press" and CBS' "Face the Nation." Levin and Graham were on CBS.
The Associated Press contributed to this report.